ES9 Additional Exercises Chapter 1

1. Determine which of the following statements is descriptive in nature and which is inferential. a. 99% of all big and tall travelers dislike cramped airline seating the most.b. 99% of the 10,000 King-Size Co. customers dislike cramped airline seating the most.

2. The Design, Sample, and Method section of an article titled "Making Behavior Changes After a Myocardial Infarction" (Western Journal of Nursing Research, Aug. 1993) discusses the selection of 16 informants who constituted 8 family dyads. The article states that, "to initiate contact with informants, names of persons who met the criteria were obtained from the medical records of a cardiac rehabilitation center in central Texas. Potential informants were then contacted by telephone to obtain preliminary consent. Confidentiality and anonymity of informants were ensured by coding the data to identify informants and link dyads."a. Is this a judgment sample or a probability sample?b. Is it appropriate to perform statistical inference using this sample? Justify your answer.

3. The August 29/September 5, 1994 issue of U.S. News & World Report references a study by health economists at the University of Southern California that indicated that Alzheimer's disease cost the nation $82.7 billion a year in medical expenses and lost productivity. Patients' earning loss was $22 billion, the value of time of unpaid caregivers was $35 billion, and the cost of paid care was $24 billion.a. What is the population?b. What is the response variable?c. What is the parameter?d. What is the statistic?

4. A USA Snapshot from USA Today (Nov. 1, 1994) described the greatest sources of stress in starting a company. According to the snapshot, the CEOs of Inc. magazine's 500 fastest-growing private companies gave the following responses: 50% said company finances, 23% said the need to succeed, 10% said time commitments, 9% said personal relationships, and 8% were classified as "other." Would the data collected and used to determine these percentages be classified as qualitative or quantitative?

5. The June 1994 issue of Good Housekeeping reported on a study on rape. The study found that women who screamed, bit, kicked, or ran were more likely to avoid rape than women who tried pleading, crying, or offered no resistance, and they were no more apt to be injured. The authors, however, cautioned that the study could not be interpreted as proof that all women should forcefully resist. The study involved 150 Omaha, Nebraska, police reports of rape or attempted rape.a. Are the data in this study attribute or numerical?b. Is this a judgment or a probability sample?

Chapter 2

1. The USA Snapshot ® "How to say I love you" reports the results of a David Michaelson & Associates survey for Ethel M Chocolates, on the best way to show affection.

Best way to show affection Give gift Hold hands Hugging/kissing Smiling OtherPercent who said 10% 10% 51% 20% 9%

Draw a Pareto diagram picturing this information.

2. The January 10, 1991, USA Snapshot ® "What's in U.S. landfills" reports the percentages for each type of waste in our landfills: food-4%, glass-2%, metal-14%, paper-38%, plastic-18%, yard waste-11%, other-13%.a. Construct a Pareto diagram displaying this information.b. Because of the size of the "other" category, the Pareto diagram may not be the best graph

to use. Explain why, and describe what additional information is needed to make the Pareto diagram more appropriate.

3. The closing prices (nearest dollar) of the first 50 common stocks listed in the New York Stock Exchange with a value between $10 and $99 on July 23, 1998 was as follows:

30 26 41 11 28 47 35 17 19 1726 72 26 58 16 65 13 22 45 4813 24 31 17 52 12 17 31 11 5275 37 36 35 12 75 38 32 14 5452 90 57 22 21 28 25 52 27 43

Source: USA Today, July 23, 1998. p. 5B.a. Construct a stem-and-leaf plot of these data.b. Use the plot to determine the lowest and the highest stock price from those selected.c. What price interval defined by the plot contains the most values?

4. In the May 1990 issue of the journal Social Work, the following ungrouped frequency distribution was used to represent the "size of families":

Number of Children Number of Mexican- Living at Home American Women

0 231 222 173 74 1

Source: copyright 1990, National Association of Social Workers, Inc. Social Worka. Which column represents the "size" of families? the "frequency" of those sizes?b. Construct a frequency histogram of this distribution.(Retain these answers for use in Exercise 2.21.)

5. All of the third-graders at Roth Elementary School were given a physical-fitness strength test. These data resulted:12 22 6 9 2 9 5 9 3 5 16 1 2218 6 12 21 23 9 10 24 21 17 11 18 1917 5 14 16 19 19 18 3 4 21 16 20 1514 17 4 5 22 12 15 18 20 8 10 13 20 6 9 2 17 15 9 4 15 14 19 3 24a. Construct a dotplot.b. Prepare a grouped frequency distribution using classes 1-4, 4-7, and so on, and draw a

histogram of the distribution. c. Prepare a grouped frequency distribution using classes 0-3, 3-6, 6-9, and so on, and draw a

histogram of the distribution.d. Prepare a grouped frequency distribution using class boundaries -2.5, 2.5, 7.5, 12.5 and so

on, and draw a histogram of the distribution.e. Prepare a grouped frequency distribution using classes of your choice, and draw a

histogram of the distribution.f. Describe the shape of the histogram found in (b), (c), (d), and (e) separately. Relate the

distribution seen in the histogram to the distribution seen in the dotplot.g. Discuss how the number of classes used and the choice of class boundaries used affect the

appearance of the resulting histogram.

6. The following 40 amounts are the fees that Fast Delivery charged for delivering small freight items last Thursday afternoon.

4.03 3.56 3.10 6.04 5.62 3.16 2.93 3.82 4.30 3.864.57 3.59 4.57 5.16 2.88 5.02 5.46 3.87 6.81 4.913.62 3.62 3.80 3.70 4.15 4.07 3.77 5.77 7.86 4.634.81 2.86 5.02 5.24 4.02 5.44 4.65 3.89 4.00 2.99

a. Classify these data into a grouped frequency distribution.b. Construct a relative frequency histogram of these data.

7. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291, 2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013.a. Find the mean in-state tuition and fees per school year.b. Find the median in-state tuition and fees per school year.c. Find the midrange in-state tuition and fees per school year.c. Find the mode, if one exists, per school year.

8. Atlantic Monthly (Nov. 1990) contains an article titled "The Case for More School Days." The number of days in the standard school year is given for several different countries as follows:

Country n(days)/yr Country n(days)/year Japan 243 New Zealand 190West Germany 226-240 Nigeria 190South Korea 220 British Columbia 185Israel 216 France 185Luxembourg 216 Ontario 185Soviet Union 211 Ireland 184

Netherlands 200 New Brunswick 182Scotland 200 Quebec 180Thailand 200 Spain 180Hong Kong 195 Sweden 180England/Wales 192 United States 180Hungary 192 French Belgium 175Swaziland 191 Flemish Belgium 160Finland 190

a. Find the mean and median number of days per year of school for the countries listed. (Use the midpoint of the 226-240 interval for West Germany when computing your answers.)

b. Construct a stem-and-leaf display of these data.c. Describe the relationship between the mean and the median and what properties of the data

cause the mean to be larger than the median.(Retain solution for use in answering Exercise 2.12.)

9. USA Today, July 22, 1998, reported the following statistics about the average in-season daily greens fees by state at US golf courses.

Highest: Hawaii, $85.70 Lowest: South Dakota, $23.80a. Based on this information, find the "average" of the 50 state average fees.b. Explain why your answer in part (a) is the only average value you can determine from

the given information.c. If you were told the mean value of the 50 state averages is $37.30, what can you tell about

their distribution.

10. USA Today, 10-28-94, reported on the average annual pay received by all workers covered by state and federal unemployment insurance for the 50 states. Connecticut had the highest with $33,169, South Dakota had the lowest with $18,613.a. Estimate the national average with the midrange for the states.b. The national average was reported to be $26,362. What can you conclude about the

distribution of the state averages based on the relationship between the midrange and the national average?

11. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291, 2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013. Find the following:a. variance s² b. standard deviation s

12 a. Find the range and the standard deviation for the number of days per year of school, using the data in Exercise 2.8.

b. Draw lines on the stem-and-leaf diagram drawn in answering Exercise 2.8 that represent the range and the standard deviation. Remember, the standard deviation is a measure for the mean.

c. Describe the relationship among the distribution of the data, the range, and the standard deviation.

13. A 1993 issue of Library Journal (Vol. 118, No. 17) gives the following table for the salaries of minority placements by type of library.

Library Type Number Average Salary Academic 46 $27,825Public 34 24,657School 23 30,336Special 16 29,406Other 4 25,200

a. Find the total of all salaries for the above 123 individuals.b. Find the mean salary for the above 123 individuals.c. What is the modal library type? Explain.d. Find the standard deviation for the above 123 salaries.

14. A research study of manual dexterity involved determining the time required to complete a task. The time required for each of 40 disabled individuals is as follows (data are ranked):

7.1 7.2 7.2 7.6 7.6 7.9 8.1 8.1 8.1 8.3 8.3 8.4 8.4 8.9 9.0 9.0 9.1 9.1 9.1 9.1 9.4 9.6 9.9 10.1 10.1 10.1 10.2 10.3 10.5 10.711.0 11.1 11.2 11.2 11.2 12.0 13.6 14.7 14.9 15.5

Find: a. Q1 b. Q2 c. Q3 d. P95 e. the 5-number summary f. Draw the box-and-whisker display.

15. Consider the following set of ignition times that were recorded for a synthetic fabric.30.1 30.1 30.2 30.5 31.0 31.1 31.2 31.3 31.3 31.431.5 31.6 31.6 32.0 32.4 32.5 33.0 33.0 33.0 33.534.0 34.5 34.5 35.0 35.0 35.6 36.0 36.5 36.9 37.037.5 37.5 37.6 38.0 39.5

Find: a. the median b. the midrange c. the midquartile d. the 5-number summary e. Draw the box-and-whisker display.

16. In a study involving mastery learning (Research in Higher Education, Vol. 20, No. 4, 1984), 34 students took a pretest. The mean score was 11.04, and the standard deviation was 2.36. Find the z-score for scores of 9 and 15 on the 20-question pretest.

17. An article titled "Computer-Enhanced Algebra Resources: The Effects on Achievement and Attitudes" (International Journal of Math Education in Science and Technology, 1980, Vol. 11, No. 4) compared algebra courses that used computer-assisted instruction with courses that do not. The scores that the computer-assisted instruction group made on an achievement test consisting of 50 problems had these summary statistics: n = 57, = 23.14, s = 7.02.a. Find the limits within which at least 75% of the scores fell.b. If the scores are normally distributed, what percentage of the scores will be below 30.16?

18. Below is a sample of one-way commute times, to the nearest minute, for 50 college students who are gainfully employed.

2 10 3 5 1 19 14 3 15 12 30 10 2 8 19 17 12 29 21 2915 23 3 24 4 16 49 15 64 5 3 22 19 1 48 4 25 7 22 4 3 10 33 12 14 30 10 13 5 23

a. Construct three different kinds of graphs for this data.b. Find the five measures of central tendency.c. Find the three measures of dispersion.d. Using one graph from part (a), one measure of central tendency from part (b) and one

measure of dispersion from part (c), write a short presentation of the 50 data that you believe best describes the typical employed college student's commute to work.

e. Explain how the graph and the two statistics used in answering part (d) best describe the situation.

19. Compute the mean and the standard deviation for the following set of data. Then find the percentage of the data that is within two standard deviations of the mean.

1 | .4 .7 .12 | .4 .53 | .5 .0 .4 .14 | .45 | .5 .8 .76 | .8 .8 .2 .8 .67 | .58 |9 | .4

20. Ask one of your instructors for a list of exam grades (15 to 25 grades) from a class.a. Find five measures of central tendency.b. Find the three measures of dispersion.c. Construct a stem-and-leaf display. Does this diagram suggest that the grades are normally

distributed?d. Find the following measures of location: (1) Q1 and Q3, (2) P15 and P60, (3) the standard

score z for the highest grade.

21. In the May 1990 issue of the journal Social Work, Marlow reports the following results:Number of Children Mexican- Anglo-

Living at Home American Women American Women 0 23 381 22 92 17 153 7 9

4 1 1 Copyright 1990, National Association of Social Workers, Inc. Social Work.

a. Construct a frequency histogram for each of the preceding distributions. Draw them on the same axis, using two different colors, so that you can compare their distributions. (See Exercise 2.4.)

b. Calculate the mean and standard deviation for the Mexican-American data.c. Calculate the mean and standard deviation for the Anglo-American data.d. Do these two distributions seem to be different? Cite specific reasons for your answer.

22. Mutual funds attract millions of private investors every year. USA Today assembles a Mutual Fund Scoreboard that lists 15 of the largest stock funds available and a Mutual Fund Spotlight that shows the 14 top yielding growth and income funds during the past four weeks. Three more funds were selected randomly from the general listing of all mutual funds. Midway through 1998, the combined lists are shown below, together with each fund’s total return for the year:

Fund Name Total Return (%) Fund Name Total Return (%)Fidelity Magellan 22.0 Berkshire Cap Gro & Value 41.1Vanguard Index 500 Port 20.9 Marsico Growth & Income 39.3Washington Mutual Inv 14.6 Nations Mars Gro & Inc 39.2Investment Co of America 15.7 Strong Blue Chip 100 Fund 30.9Fidelity Growth & Income 19.5 Janus Growth & Income 29.8Fidelity Contrafund 23.0 Excelsior Inst Value Equity 22.3Vanguard Windsor II 16.2 Schroder Large Cap Equity 26.7Amer Cent/20th C Ultra 30.4 Strong Total Return Fund 24.6Vanguard Wellington 9.7 Reynolds Blue Chip Growth 35.1Fidelity Puritan 13.0 Diversified Investors 30.1Fidelity Equity-Inc 12.9 Strong Growth & Income 26.9Fidelity Adv Growth Oppty 14.5 Newpoint Equity Fund 23.6Vanguard Windsor 10.1 New Providence Cap Gro 10.9Income Fund of America 6.9 Weitz Partners Value Fund 30.2Janus Fund 26.2 Putnam High Yield 4.6Pioneer Capital Growth 8.0 Standish Internat’l Equity 30.1

Source: USA Today, July 23, 1998, pp. 3B,6B.

a. Omit names and build a 4 x 8 table of ranked total return percentages in ascending order, reading vertically in each column.

b. Construct a 5-number summary table.c. Find the midquartile total return percentage and the interquartile range.d. What are the z-scores for Berkshire Capital Growth & Value, Income Fund of America, and

Janus Fund?e. Based on the data and your calculations, can you pinpoint the three funds selected at

random?

Chapter 3

1. In a study involving children's fear related to being hospitalized, the age and the score each child made on the Child Medical Fear Scale (CMFS) were:Age (x) 8 9 9 10 11 9 9 9 11 11CMFS score (y) 31 25 40 27 35 29 25 34 27 36Construct a scatter diagram of these data. (Retain for use in answering Exercise 3.4.)

2. Walter Payton was one of the NFL's greatest running backs. Below are listed the number of carries and the total yards gained in each of his 13 years with the Chicago Bears.Number Carries 196 311 339 333 369 317 339 148 314 381 324 321 146Total Yards 679 1390 1852 1359 1610 1460 1222 596 1421 1684 1551 1333 586a. Construct a scatter diagram depicting these data.b. How would you describe this scatter diagram? What do you see that is unusual about the

scatter diagram?c. What circumstances might explain this "two group" appearance of the data points? Explain.

3. Total solar eclipses actually take place nearly as often as total lunar eclipses, but they are visible over a much narrower path. Both the path width and the duration vary substantially from one eclipse to the next. The table below shows the duration (seconds) and path width (miles) of 44 total solar eclipses measured in the past and those projected to the year 2010:

Date Duration (s) Width (mi) Date Duration (s) Width (mi)1950 73 83 1983 310 1231952 189 85 1984 119 531954 155 95 1985 118 4301955 427 157 1986 1 11956 284 266 1987 7 31958 310 129 1988 216 1041959 181 75 1990 152 1251961 165 160 1991 413 1601962 248 91 1992 320 1821963 99 63 1994 263 1171965 315 123 1995 129 481966 117 52 1997 170 2211968 39 64 1998 248 941970 207 95 1999 142 691972 155 109 2001 296 1251973 423 159 2002 124 541974 308 214 2003 117 3381976 286 123 2005 42 171977 157 61 2006 247 1141979 169 185 2008 147 1441980 248 92 2009 399 1601981 122 67 2010 320 160

Source: The World Almanac and Book of Facts 1998, p. 296.a. Draw a scatter diagram showing duration, y, and path width, x, for the total solar eclipses.b. How would you describe this diagram?

4. In an article titled "Self-Reported Fears of Hospitalized School-Age Children" (Journal of Pediatric Nursing, Vol. 9, No. 2, 1994), the authors report a correlation of 0.10 between the ages of children and the score they made on the Child Medical Fear Scale (CMFS). Suppose the ages and CMFS scores for ten children were as follows (same data as Exercise 3.1):CMFS Score 31 25 40 27 35 29 25 34 27 36Age 8 9 9 10 11 9 9 9 11 11Find: a. SS(x) b. SS(y) c. SS(xy) d. the value of r for these data

5. Consider the following data, which give the weight (in thousands of pounds) x and gasoline mileage (miles per gallon) y for ten different automobiles.

x 2.5 3.0 4.0 3.5 2.7 4.5 3.8 2.9 5.0 2.2y 40 43 30 35 42 19 32 39 15 44

Find: a. SS(x) b. SS(y) c. SS(xy) d. Pearson's product moment r

6. An article titled "Leader Power, Commitment Satisfaction, and Propensity to Leave a Job Among U.S. Accountants" (Journal of Social Psychology, Vol. 133, No. 5, Oct. 1993) reported a linear correlation coefficient of -0.61 between satisfaction with work scores and propensity to leave a job scores. Suppose similar assessments of work satisfaction, x, and propensity to leave a job, y, gave the following scores.

x 12 24 17 28 24 36 20y 44 36 25 23 32 17 24

a. Find the linear correlation between x and y.b. What does the value of this correlation coefficient seem to be telling us? Explain.

7. Cable television video networks can be measured on the basis of both their number of noncable affiliates and number of subscribers. Below is a table of 18 video networks, their affiliates and subscribers (in millions):

Network Affiliates SubscribersESPN-1 27,600 71.1CNN 11,528 71.0TNT 10,538 70.5TBS 11,668 69.9C-SPAN 6,003 69.7USA Network 12,500 69.7TNN 17,636 68.9LIFETIME Television 8,300 67.0The Family Channel 13,352 66.9Arts & Entertainment 12,000 66.9MTV: Music Television 9,176 66.7Nickelodian 11,788 66.0Nick at Nite 11,711 66.0The Weather Channel 6,500 64.2Headline News 6,470 64.0CNBC 11,711 60.0QVC Network 5,895 58.2VH-1 6,088 56.3

Source: Cable Television Developments, National Cable Television Assn., Jan.-Mar. 1997.a. Draw a scatter diagram of the two variables, affiliates and subscribers.b. Find the linear correlation coefficient and interpret the results.

8. An article titled "College Recreation Facility Survey" (Athletic Business, April 1994) reported the following results from 358 four-year colleges and universities in the United States and Canada.

Total Square Feet Devoted Enrollment Number of Schools to Recreation per School

0 - 1,249 58 47,864 1,250 - 2,499 53 71,828 2,500 - 4,999 53 89,716 5,000 - 9,999 62 101,01610,000 - 17,999 68 127,95218,000 or over 64 200,896

a. Using the midpoint of the first five enrollment classes and 25,000 in place of the class 18,000 or over for the x-values and the total square feet devoted to recreation per school for the y-values, find the linear correlation coefficient between x and y.

b. What does the value of this correlation seem to be telling us? Explain.

9. An article titled "Microbioluminometry Assay (MBA): Determination of Erythromycin Activity in Plasma or Serum" (Journal of Pharmaceutical sciences, Dec. 1989) compares the MBA assay with another method, agar diffusion plate assay, for determining the erythromycin activity in plasma or serum. The MBA technique is economical because it requires less sample and reagents.If X represents the agar diffusion plate assay in micrograms per milliliter and Y represents the MBA assay in micrograms per milliliter, then the results may be expressed as

Y = 0.054128 + 0.92012X r = 0.9525 n = 206If the agar diffusion plate assay determined the level of erythromycin to be 1.200, predict what the MBA assay would be.

10. In the article "Beyond Prediction: The Challenge of Minority Achievement in Higher Education" (Lunneborg and Lunneborg, Journal of Multicultural Counseling and Development), the relationship between high school GPA and first-year university GPA was investigated for the following groups: Asian Americans, blacks, chicanos, Native Americans, and whites. For the 43 Native Americans, the correlation was found to be 0.26 and the equation of the line of best fit was found to be university GPA = 1.85 + 0.30 high school GPA. Both GPAs were 4.0 scales.Use the equation of the line of best fit to predict the mean first-year-university GPA for all Native Americans who had a high school GPA equal to 3.0.

11. People not only live longer today but also live longer independently. The May/June 1989 issue of Public Health Reports published an article titled "A Multistate Analysis of Active Life Expectancy." Two of the variables studied were a person's current age and the expected number of years remaining.Age x 65 67 69 71 73 75 77 79 81 83Years Remaining y 16.5 15.1 13.7 12.4 11.2 10.1 9.0 8.4 7.1 6.4a. Draw a scatter diagram.b. Calculate the equation of best fit.c. Draw the line of best fit on the scatter diagram.d. What is the expected years remaining for a person who is 70 years old? Find the answer in

two different ways: Use the equation from (b) and use the line on the scatter diagram from (c).

e. Are you surprised that the data all lie so close to the line of best fit? Explain why the ordered pairs follow the line of best fit so closely.

12. A record of maintenance costs is kept for each of several cash registers throughout a department store chain. A sample of 14 registers gave the following data:

Age x Maintenance Cost y | Age x Maintenance Cost y (years) (dollars) | (years) (dollars)

6 142 | 2 997 231 | 1 1141 73 | 9 1913 90 | 3 1606 176 | 8 1554 132 | 9 2315 167 | 8 202

a. Draw a scatter diagram that shows these data.b. Calculate the equation of the line of best fit.c. A particular cash register is eight years old. How much maintenance (cost) do you predict it

will require this year?d. Interpret your answer to (c).

13. The following data are the ages and the asking prices for 19 used foreign compact cars:Age x Price y | Age x Price y(years) (x $100) | (years) (x $100)

3 68 | 6 425 52 | 8 223 63 | 5 506 24 | 6 364 60 | 5 464 60 | 7 366 28 | 4 487 36 | 7 202 68 | 5 362 64 |

a. Draw a scatter diagram.b. Calculate the equation of the line of best fit.c. Graph the line of best fit on the scatter diagram.d. Predict the average asking price for all such foreign cars that are five years old. Obtain this

answer in two ways: Use the equation from (b) and use the line drawn in (c).

14. An article titled "Women, Work and Well-Being: The Importance of Work Conditions (Health and Social Behavior, Vol. 35, No. 3, Sept. 1994) studied 202 full-time homemakers and 197 employed wives. The linear correlation coefficient between family income and education was reported to equal 0.43 for the participants in the study. A similar study involving eight individuals gave the following results. (x represents the years of education, and y represents the family income in thousands of dollars).

x 12 13 10 14 11 14 16 16y 34 45 36 47 43 35 50 42

a. Find the linear correlation between x and y.b. Find the equation of the line of best fit.

15. You have probably thought about the number of hours you spend at work or at leisure, but have you ever wondered about the relationship between the number of hours that all Americans spend per week at work and at leisure?

Year Work Leisure1995 50.6 19.21993 50.0 19.01989 48.7 16.61984 47.3 16.61980 46.9 19.21975 43.1 24.3USA Today December 26, 1996

a. How many hours did you, personally, spend working last week? How many hours did you spend at leisure pursuits?

b. Construct one graph using years as a horizontal axis, hours as the vertical axis and plot hours of work and hours of leisure using two different colored dots. Connect the dots.

c. Do you see any pattern(s) to the graph? Explain. d. Is there a relationship between the two variables, hours spent at work and hours devoted to

leisure? When people spend more time at one, do they spend less time at the other? Use the techniques learned in this chapter to present graphic and numerical statistics that aid in the explanation of your answer to these questions.

16. "Fast-Food Fat Counts Full of Surprises," in USA Today, 10-20-94, compared some of the popular fast-food items in calories and fat.Calories (x) 270 420 210 450 130 310 290 450 446 640 233Fat (y) 9 20 10 22 6 25 7 20 20 38 11

x 552 360 838 199 360 345 552 y 55 6 20 12 36 28 22a. Draw a scatter diagram of these data.b. Calculate the linear coefficient, r.c. Find the equation of the line of best fit.d. Explain the meaning of the above answers.

17. A biological study of a minnow called the blacknose dace was conducted. The length, y, in millimeters and the age, x, to the nearest year were recorded.

x 0 3 2 2 1 3 2 4 1 1y 25 80 45 40 36 75 50 95 30 15

a. Draw a scatter diagram of these data.b. Calculate the correlation coefficient.c. Find the equation of the line of best fit.d. Explain the meaning of the above answers.

18. Investors in mutual funds keep a sharp eye on the total return on their money. They also are aware of the risk involved in their investment, commonly measured by a fund’s volatility (the greater the volatility, the higher the risk). Below is a list of 30 mutual funds randomly selected in 1998 from Fortune’s list of stock and bond funds, together with their 5-year total return (%) and risk assessment:

Fund Name Total Return Risk Fund Name Total Return RiskMFS Emerging Growth 21.5 20.6 AIM Balanced A 15.9 10.8Kaufmann 19.7 18.4 Greenspring 14.0 7.2AIM Constellation A 17.6 18.4 Delaware A 13.6 8.6Weitz Hickory 29.9 19.7 Calamos Convertible A 14.3 9.9Oak Value 25.6 13.0 Managers Bond 10.3 5.4Gabelli Westwood Equity 23.0 12.3 Harbor Bond 7.3 4.4Nationwide 24.3 12.0 Northeast Investors 13.6 5.5Fidelity Growth/Income 22.6 13.0 Strong Gov’t. Securities 7.0 4.4Stratton Growth 21.3 11.8 Lexington GNMA Income 6.9 3.5GAM International A 22.6 19.9 Marshall Gov’t. Income 5.8 3.7Scudder International 14.3 13.7 Wright U.S. Treasury 6.3 7.5Janus Worldwide 23.6 13.7 Excelsior Tax-Exempt 7.6 6.7Oppenheimer Global A 19.0 14.4 Vanguard Municipal 6.5 5.5New Perspective 18.8 12.1 Goldman Sachs Global 7.2 4.1Putnam Europe Growth A 22.7 14.6 Capital World Bond 5.9 4.9

Source: Fortune, “The Best Mutual Funds”, August 17, 1998, pp. 88-98.

a. Draw a scatter diagram with 5-year total return as the y-axis and risk as the x-axis.b. Calculate the correlation coefficient.c. Would you conclude that in order to obtain higher total returns, mutual fund investors must

take greater risks? Explain.

Chapter 4

1. An article titled "Pain and Pain-Related Side Effects in an ICU and on a Surgical Unit: Nurses' Management" (American Journal of Critical Care, January 1994, Vol. 3, No. 1) gave the following table summarizing the study participants. (Note: ICU is an acronym for intensive care unit.)

Gender ICU Surgical UnitFemale 9 6Male 11 18

One of these participants is randomly selected. Answer the following questions.a. Are the events "being a female" and "being in the ICU" mutually exclusive?b. Are the events "being in the ICU" and "being in the surgical unit" mutually exclusive?c. Find P(ICU or female).c. Find P(ICU or male).

2. Tracy Shark walked into the card room at her country club and played one hand of bridge at one table and one hand of poker at another table. She was dealt a bridge hand with all 13 cards in the same suit, and then she was dealt a poker hand with a royal flush. As she left the room shaking her head, she was overheard mumbling, “I doubt that will happen again in a million years.” Assuming the decks were shuffled and the dealers were straight, compute the probability of the joint occurrence of the two events. Do you agree with Tracy?

3. The December 1994 issue of The American Spectator quotes a poll by the Times-Mirror Center for the People and the Press as finding that 71% of Americans believe that the press "gets in the way of society solving its problems."a. If two Americans are randomly selected, find the probability that both will believe that the

press "gets in the way of society solving its problems."b. If two Americans are selected, find the probability that neither of the two will believe that the

press "gets in the way of society solving its problems."c. If three are selected, what is the probability that all three believe the press gets in the way?

4. The August 1, 1994, issue of The New Republic gives the results of a U.S. Justice Department study which states that among white spousal murder victims, 62% are female. If the records of three victims are randomly selected from a large data base of such murder victims, what is the probability that all three victims are male?

5. An article involving smoking cessation intervention in Heart & Lung (March/April 1994, Vol. 23, No. 2) divided 80 subjects into a two-way classification:

Diagnosis Group Cardiovascular Oncology General Surgery Experimental 10 14 13Usual Care 12 16 15

Suppose one of these 80 subjects is selected at random. Find the probabilities of the following events.a. The subject is not in the experimental group.b. The subject is in the experimental group and has oncology diagnosis.c. The subject is in the experimental group or ha a cardiovascular diagnosis.

6. A study concerning coping strategies of abstainers from alcohol appeared in Image, the Journal of Nursing Scholarship (Vol. 25, No. 1, Spring 1993). The study involved 23 subjects who were classified according to sex as well as marital status as shown in the table.

Marital Status Men WomenCurrently married 10 3Divorced/separated 3 6Never married 1 0

One of the subjects is selected at random. Find:a. The probability the subject is currently married given that the individual is a man.b. The probability the subject is a woman given that the individual is divorced/separated.c. The probability the subject is a man given that the individual has never married.

7. An article titled "A Puzzling Plague" found in the January 14, 1991, issue of Time, stated that one out of every ten American women will get breast cancer. It also states that of those who do, one out of four will die of it. Use these probabilities to find the probability that a randomly selected American woman willa. never get breast cancer.b. get breast cancer and not die of it.c. get breast cancer and die from it.

8. The Pennsylvania Lottery game big 4 has been played for more than 18 years. The table below lists the number of times each single-digit number was the winning number for each of the four positions. The frequencies for each number in each position range from 304 to 367.

Number First Second Third Fourth Total0 343 312 352 328 13351 326 330 351 357 13642 347 323 315 344 13293 320 327 350 351 13484 304 345 331 318 12985 321 348 322 343 13346 339 306 329 316 12907 348 346 351 311 13568 337 367 329 350 13839 360 341 315 327 1343

a. Do the frequencies of each number as a winner in the first position appear to indicate that the numbers occur randomly as first position winners? What statistical evidence can you find to justify your answer? Present a convincing case.

b. Do the frequencies of each number as a winner in the second, third and fourth positions appear to indicate that the numbers occur randomly as position winners? What statistical evidence can you find to justify your answer? Present a convincing case.

c. Each single-digit number has appeared as a winning number a different number of times ranging from 1290 to 1383. Do you think these numbers vary sufficiently to make a case that the digits do not occur with equal probability? Present evidence to support your answer.

9. According to the National Cancer Data Base report for Hodgkin's disease (CA-A Cancer Journal for Clinicians, Jan./Feb. 1991), the highest percentage of patients (31%) were 20 to 29 years of age, and they had a three-year observed survival rate of 91%. What is the probability that an individual who has been diagnosed with Hodgkin's disease is between 20 and 29 years of age and will survive for three years?

Chapter 5

1. "How women define holiday shopping," a USA Snapshot® (12-9-94) reported that 50% said "a pleasure," 22% said "a chore," 19% said "no big deal," and 8% said "a nightmare." The percentages do not sum to 100% due to round-off error.a. What is the variable involved, and what are the possible values?b. Why is this variable not a random variable?

2. "Kids who smoke," a USA Snapshot (4-25-94), reports the percentage of children in each age group who smoke.

Age, x Percent Who Smoke 12 1.713 4.914 8.915 16.316 25.217 37 .2

Is this a probability distribution? Explain why or why not.

3. A USA Snapshot® (11-1-94) titled "How many telephones we have" reported that 1% have none, 11% have one, 31% have two, and 57% have three or more. Let x equal the number of phones per home, and replace the category "three or more" with exactly "three."a. Find the mean and standard deviation for the random variable x.b. Explain the effect of replacing the category "three or more" with "three" had on the

distribution of x, the mean, and the standard deviation.

4. a. Use the probability distribution shown below and describe in your own words how the mean of the variable x is found.

x 1 2 3 4P(x) 0.1 0.2 0.3 0.4

b. Find the mean of x. c. Find the deviation from the mean for each x-value.d. Find the value of each "squared deviation from the mean."e. Recalling your answer to (a), find the mean of the variable "squared deviation."f. "Variance" was the name given to the "mean of the squared deviations." Explain how formula (5.2) expresses the variance as a mean.

5. In California, 30% of the people have a certain blood type. What is the probability that exactly 5 out of a randomly selected group of 14 Californians will have that blood type? (Find the answer by using a table.)

6. On the average, 1 out of every 10 boards purchased by a cabinet manufacturer is unusable for building cabinets. What is the probability that 8, 9, or 10 of a set of 11 such boards are usable? (Find the answer by using a table.)

7. A local polling organization maintains that 90% of the eligible voters have never heard of John Anderson, who was a presidential candidate in 1980. If this is so, what is the probability that in a randomly selected sample of 12 eligible voters, 2 or fewer have heard of John Anderson?

8. A basketball player has a history of making 80% of the foul shots taken during games. What is the probability that he will miss three of the next five foul shots he takes?

9. According to an article in the February 1991 issue of Reader's Digest, Americans face a 1 in 20 chance of acquiring an infection while hospitalized. If the records of 15 randomly selected hospitalized patients are examined, find the probability thata. none of the 15 acquired an infection while hospitalized.b. 1 or more of the 15 acquired an infection while hospitalized.

10. An article in the Omaha World-Herald (12-1-94) stated that only about 60% of the individuals needing a bone marrow transplant find a suitable donor when they turn to registries of unrelated donors. In a group of 10 individuals needing a bone marrow transplant,a. what is the probability that all 10 will find a suitable donor among the registries of unrelated

donors?b. what is the probability that exactly 8 will find a suitable donor among the registries of

unrelated donors?c. what is the probability that at least 8 will find a suitable donor among the registries of

unrelated donors?d. what is the probability that no more than 5 will find a suitable donor among the registries of

unrelated donors?

11. Colorado Rockies baseball player Larry Walker’s league-leading batting average reached .344 after 415 times at bat during the 1998 season (ratio of hits to at bats). Suppose Walker has five official times at bat during his next game. Assuming no extenuating circumstances and that the binomial model will produce reasonable approximations, what is the probability that Walker:a. gets less than two hits?b. gets more than three hits?c. goes five-for-five (all hits)?

12. According to Financial Executive (July/August 1993) disability causes 48% of all mortgage foreclosures. Given that 20 mortgage foreclosures are audited by a large lending institution,a. find the probability that 5 or fewer of the foreclosures are due to a disability.b. find the probability that at least 3 are due to a disability.

13. Seventy-five percent of the foreign-made autos sold in the United States in 1984 are now falling apart.a. Determine the probability distribution of x, the number of these autos that are falling apart in

a random sample of five cars.b. Draw a histogram of the distribution.c. Calculate the mean and standard deviation of this distribution.

14. A 1998 survey conducted by Fortune revealed that the Marriott International workforce was composed of 50.3% minorities. A further subdivision revealed 6.0% Asian, 24.2% black, and 19.6% Hispanic. Source: Fortune, “The Diversity Elite”, August 3, 1998, p. 114.Find the mean and standard deviation of all samples of 25 randomly selected employees of the Marriott International workforce for each of the three minority groups. Present your statistics in a table.

15. A USA Snapshot® titled "Stress does not love company" (11-3-94) answered the question "How people say they prefer to spend stressful times." Forty-eight percent responded "alone," 29% responded "with family," 18% responded "with friends," and 5% responded "other/don't know." Ten individuals are randomly selected and asked the question "How do you prefer to spend stressful times?"a. What is the probability that two or fewer will respond by saying "alone"?b. Explain why this question can be answered using binomial probabilities.

16. For years, the manager of a certain company had sole responsibility for making decisions with regards to company policy. This manager has a history of making the correct decision with a probability of p. Recently company policy has changed, and now all decisions are to be made by majority rule of a three-person committee.a. Each member makes a decision independently, and each has a probability of p of making

the correct decision. What is the probability that the committee's majority decision will be correct?

b. If p = 0.1, what is the probability that the committee makes the correct decision?c. If p = 0.8, what is the probability that the committee makes the correct decision?d. For what values of p is the committee more likely to make the correct decision by majority

rule than the former manager?e. For what values (there are three) of p is the probability of a correct decision the same for the

manager and for the committee? Justify your answer.

17. Suppose one member of the committee in Exercise 5.16 always makes the decision by rolling a die. If the die roll results in an even number, they vote for the proposal, and if an odd number occurs, they vote against it. The other two members still decide independently and have a probability of p of making the correct decision.a. What is the probability that the committee's majority decision will be correct?b. If p = 0.1, what is the probability that the committee makes the correct decision?c. If p = 0.8, what is the probability that the committee makes the correct decision?d. For what value of p is the committee more likely to make the correct decision by majority

rule than the former manager?e. For what values of p is the probability of a correct decision the same for the manager and for

the committee? Justify your answer.f. Why is the answer to (e) different than the answer to Exercise 5.16 (e)?

Chapter 6

1. According to the November 1993 issue of Harper's magazine, our kids spend from 1200 to 1800 hours a year in front of the television set. Suppose the time spent by kids in front of the television set per year is normally distributed with a mean equal to 1500 hours and a standard deviation equal to 100 hours.a. What percentage spend between 1400 and 1600 hours?b. What percentage spend between 1300 and 1700 hours?c. What percentage spend between 1200 and 1800 hours?c. Compare the results (a) through (c) with the empirical rule. Explain the relationship.

2. For a particular age group of adult males, the distribution of cholesterol readings, in mg/dl, is normally distributed with a mean of 210 and a standard deviation of 15.a. What percentage of this population would have readings exceeding 250?b. What percentage would have readings less than 150?

3. At Pacific Freight Lines, bonuses are given to billing clerks when they complete 300 or more freight bills during an eight-hour day. The number of bills completed per clerk per eight-hour day is approximately normally distributed with a mean of 270 and a standard deviation of 16. What proportion of the time should a randomly selected billing clerk expect to receive a bonus?

4. The waiting time x at a certain bank is approximately normally distributed with a mean of 3.7 min and a standard deviation of 1.4 min.a. Find the probability that a randomly selected customer has to wait less than 2.0 min.b. Find the probability that a randomly selected customer has to wait more than 6 min.d. Find the value of the 75th percentile for x.

5. According to a USA Snapshot ® (10-26-94), the average annual salary for a worker in the United States is $26,362. If we assume that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500, find the following:a. What percentage earn below $15,000?b. What percentage earn above $40,000?

6. According to the 1991 issue of American Hospital Administration Hospital Statistics, the average daily census total for 116 hospitals in Mississippi equals 10,872. Suppose the standard deviation of the daily census totals for these hospitals equals 1505 patients. If the daily census totals are normally distributed:a. What percentage of the days does the daily census total less than 8500 patients in these

hospitals? Approximately how often should we expect this to occur?b. What percentage of the days does the daily census total exceed 12,500 patients in these

hospitals? Approximately how often should we expect this to occur?

7. A drug manufacturer states that only 5% of the patients using a particular drug will experience side effects. Doctors at a large university hospital use the drug in treating 250 patients. What is the probability that 15 or fewer of the 250 patients experience side effects?

8. A survey in the March 1994 issue of Life magazine indicated that 9 out of 10 Americans pray frequently and earnestly, and almost all say God has answered their prayers. Assuming "9 out of 10" is accurate, use the normal approximation to the binomial to find the probability that in a national survey of 1000 Americans, at least 925 will indicate that they pray frequently and earnestly.

9. An article in Life magazine indicated than 60% of Americans have had a psychic experience. An example of a psychic experience is dreaming about an event before it actually occurs. Some experts call psychic experiences precognitions, whereas others write it off as pure coincidence. Suppose a national survey of 2000 Americans is conducted and each is asked whether or not they have had a psychic experience. Use the normal approximation to the binomial distribution to find the probability that over 1,230 report such a phenomenon. Source: Life, June, 1998. p. 89.

10. According to the Bureau of Justice Statistics Sourcebook of Criminal Justice Statistics 1992, 4.5% of young adults reported using alcohol daily for the past 30 days. Use the normal approximation to the binomial distribution to find the probability that, in a national poll of 1024 young adults, between 35 and 50 inclusive will indicate that they have used alcohol daily for the past 30 days.a. Solve using normal approximation and Table 3.b. Solve using a computer or calculator and the normal approximation method.c. Solve using a computer or calculator and the binomial probability function.

11. An article in USA Today (4-4-91) quoted a study involving 3365 people in Minneapolis-St. Paul between 1980 and 1982 and another 4545 between 1985 and 1987. It found that the average cholesterol level for males was 200. The authors of the study say the results of their study are probably similar nationwide. Assume that the cholesterol values for males in the United States are normally distributed with a mean equal to 200 and a standard deviation equal to 25.a. What percentage have readings between 150 and 225?b. What percentage have readings that exceed 250?

12. If 60% of the registered voters plan to vote for Ralph Brown for mayor of a large city. What is the probability that less than half of the voters, in a poll of 200 registered voters, plan to vote for Ralph brown?

Chapter 7

1. According to a USA Snapshot® (USA Today, October 21-23, 1994), the average amount spent per month for long-distance calls through the long-distance carrier is $31.65. If the standard deviation for long-distance calls through the long-distance carrier is $12.25 and a sample of 150 customers is selected, the mean of this sample belongs to a sampling distribution.a. What is the shape of this distribution?b. What is the mean of this sampling distribution?c. What is the standard deviation of this sampling distribution?

2. More Americans heat their homes with natural gas than any other fuel. According to the American Gas Association, the national average price of natural gas sold to residential customers in 1997 was 62 cents per therm, about 18 percent less than it cost ten years earlier, in inflation-adjusted dollars. Source: 1997 Gas Facts, American Gas Association.If the standard deviation for prices of natural gas sold to residential customers is 11 cents per therm and a random sample of 200 residential customers in 1997 is selected, the mean of this sample belongs to a sampling distribution.a. What is the shape of this sampling distribution?b. What is the mean of this sampling distribution?c. What is the standard deviation of this sampling distribution?

3. According to the 1993 World Factbook, the 1993 total fertility rate (mean number of children born per woman) for Madagascar is 6.75. Suppose the standard deviation of the total fertility rate is 2.5. The mean number of children for a sample of 200 randomly selected women is one value of many that form the sampling distribution of sample means.a. What is the mean value for this sampling distribution?b. What is the standard deviation of this sampling distribution?c. Describe the shape of this sampling distribution.

4. According to the 1994 World Almanac, the average speed of winds in Honolulu, Hawaii, equals 11.4 miles per hour. Assume that wind speeds are approximately normally distributed with a standard deviation of 3.5 miles per hour.a. Find the probability that the wind speed on any one reading will exceed 13.5 miles per hour.b. Find the probability that the mean of a random sample of 9 readings exceeds 13.5 miles per

hour.c. Do you think the assumption of normality is reasonable? Explain.d. What effect do you think the assumption of normality had on the answers to (a) and (b)?

Explain.

5. According to the U.S. Dept. of Energy, the average price of unleaded regular gasoline sold at service stations throughout the nation in 1996 was $1.23 per gallon. Assume that gasoline prices in general are normally distributed with a standard deviation of $.16 per gallon.

Source: Energy Administration, U.S. Dept. of Energy, Monthly Energy Review, June 1997.

A random sample of 45 stations in 1996 is selected and the pump prices for unleaded regular gasoline are recorded. Find the probability that the sample mean price:

a. exceeds $1.28 per gallon.b. is less than $1.19 per gallon.c. is between $1.20 and $1.27 per gallon.

6. According to the World Almanac and Book of Facts - 1994, the median weekly earnings of full-time wage and salary women, age 16 years or older in 1992, equals $381. Assume that the wages and salaries are normally distributed with = $85.a. Find the probability that the mean weekly earnings of a sample of 250 such women is

between $375 and $385, if the mean equals $381.b. Do you think the assumption of normality is reasonable? Explain.c. What effect do you think the assumption of normality about the x distribution had on the

answer to (a)? Explain.d. Do you think the assumption of mean equals $381 is reasonable? Explain.e. What effect do you think the assumption about the value of the mean had on the answer to

(a)? Explain.

7. According to the August 1994 issue of Employment and Earnings, the June 1994 average weekly earnings for employees in general automotive repair shops was $406.15. Suppose the standard deviation for the weekly earnings for such employees is $55.50. Assuming that this mean and standard deviation are the current values, find the following probabilities for the mean of a sample of 100 such employees.a. The probability the mean of the sample is less than $400.b. The probability the sample mean is between $400 and $410.c. The probability the mean of the sample is greater than $415.d. Explain why the assumption of normality about the x distribution was not involved in the

solution to (a), (b), and (c).

8. The Gallup Poll has been surveying the public for many years. When repeated sampling is used to track America's attitudes, the sample statistic reported, the percentage of yes responses, does not form a sampling distribution, but rather it forms a time series and demonstrates a trend. (Time series is a topic not covered in this text; however, many of its components are.) Complete the following questions to help recognize and understand the difference between repeated samples that belong to a sampling distribution and those that belong to a time series.

Year Yes No1937 34 661949 48 481955 52 441967 57 391969 54 391971 66 291975 73 231978 76 191983 80 161984 78 171987 82 122000 xx zz

a. Plot a scatter diagram displaying the Selected National Trend information (above), using the year as the input variable and the percentage of yes responses as the output variable y.

b. On the scatter diagram drawn in (a), plot the percentages of the no responses as a second output variable using the year number as the input variable x.

c. Do you see what could be called a trend? Explain.d. Make a prediction for the percentage of Americans who would vote for a woman president.

How did you use the cases study information?e. Sampling distributions involve repeated sampling from the same population, but with a

completely different purpose. Explain, in your own words, how a sampling distribution is different than the chapter case study illustration.

f. Repeated sampling, like that in the chapter case study and that used in quality control, is carried out for the purpose of "tracking" the statistic being studied. Describe, in your own words, the purpose of studying a statistic from repeated samples as a sampling distribution.

9. According to an article in Pharmaceutical News (January 1991), a person age 65 or older will spend, on the average, $300 on personal-care products per year. If we assume that the amount spent on personal-care products by individuals 65 or older is normally distributed and has a standard deviation equal to $75, what is the probability that the mean amount spent by 25 randomly selected such individuals will fall between $250 and $350?

10. A report in Newsweek (November 12, 1990) stated that the day-care cost per week in Boston is $109. If this figure is taken as the mean cost per week and if the standard deviation were known to be $20, find the probability that a sample of 50 day-care centers would show a mean cost of $100 or less per week.

Chapter 8

1. An article titled "A Comparison of the Effects of Constant Co-operative Grouping versus Variable Co-operative Grouping on Mathematics Achievement Among Seventh Grade Students," (International Journal of Mathematics Education in Science and Technology, Vol. 24, No. 5, 1993) gives the mean percentile score on the California Achievement Test (CAT) for 20 students to be 55.20. Assume the population of CAT scores is normally distributed and that = 19.5.a. Make a point estimate for the mean of the population the sample represents.b. Find the maximum error of estimate for a level of confidence equal to 95%.c. Construct a 95% confidence interval for the population mean.d. Explain the meaning of each of the above answers.

2. According to a USA Snapshot® (USA Today, 11-3-94), the annual teaching income for ski instructors in the Rocky Mountain and Sierra areas is $5600. (Assume = $1000.)a. If this figure is based on a survey of 15 instructors and if the annual incomes are normally

distributed, find a 90% confidence interval for , the mean annual teaching income for all ski instructors in the Rocky Mountain and Sierra areas.

b. If the distribution of annual incomes is not normally distributed, what effect do you think that would have on the interval answer in part (a)? Explain.

3. According to an article in Good Housekeeping (February 1991) a 128.lb woman who walks for 30 minutes four times a week at a steady, 4 mi./hr pace can lose up to 10 pounds over a span of a year. Suppose 50 women with weights between 125 and 130 lb performed the four walks per week for a year and at the end of the year the average weight loss for the 50 was 9.1 lb. Assuming that the standard deviation, , is 5, complete the hypothesis test of Ho: = 10.0 vs. Ha: 10.0 at the 0.05 level of significance using the p-value approach.

4. The gestation period (the elapsed time between conception and birth) of gray squirrels measured in captivity is listed as 44 days as estimated by the author of Walker’s Mammals of the World. It is recognized that the potential life span of animals is rarely attained in nature, but the gestation period could be either shorter or longer.

Source: Walker’s Mammals of the World 5e, Johns Hopkins University Press, 1991.Suppose the gestation period of a sample of 81 squirrels living in the wild is measured using the latest techniques available, and the mean length of time is found to be 42.5 days. Test the hypothesis that squirrels living in the wild have the same gestation period as those in captivity at the 0.05 level of significance. Assume that = 5 days. Use the classical approach.a. Define the parameter. b. State the null and alternative hypotheses.c. Specify the hypothesis test criteria. d. Present the sample evidence.e. Find the probability distribution information. f. Determine the results.

5. The USA Snapshot® “Holiday home trimmings” presented information about all American households (page 626). One hundred fifty adult shoppers at a large shopping mall were asked “How much (to the nearest $25) do you anticipate your family will spend on holiday decorations this year?”

25 200 100 25 250 75 25 50 25 100 75 25 100 75 2525 200 25 0 25 175 25 75 100 100 50 25 50 100 5025 100 100 175 25 75 25 0 100 25 25 50 25 25 75 0 100 100 75 75 100 25 50 50 25 100 100 150 75 75

25 25 50 75 75 100 25 50 0 25 25 100 25 50 150150 75 100 150 0 100 75 25 75 25 0 300 25 25 50

25 100 25 75 75 25 25 50 50 50 50 25 100 125 5050 75 25 75 25 0 100 0 50 75 50 100 50 125 2550 75 125 100 50 125 200 75 25 25 25 50 25 50 2525 0 0 100 25 100 100 50 25 25 125 25 75 100 25

Use the above sample data to describe the anticipated amount households living near this mall plan to spend on holiday decorations this year. a. Describe the sample data using several numerical statistics and at least one graph.b. Estimate the mean anticipated amount households living near this mall plan to spend on

holiday decorations this year. Use 95% level of confidence and assume = 70. c. Does the above sample suggest that the families who shop in this mall anticipate spending a

different average amount than all Americans according to “Holiday home trimmings”? Use = 0.05.

d. Are the assumptions for the confidence interval and hypothesis test methods satisfied? Explain.

Chapter 9

1. There seems to be no end to how large the signing bonuses professional athletes can obtain when they start their careers. When the Indianapolis Colts gave Peyton Manning $11.6 million and the San Diego Chargers awarded Ryan Leaf $11.25 million as signing bonuses in 1998, both these amounts exceeded what the 1989 first round draft pick, Troy Aikman, earned in his first five National Football League seasons combined while playing for the Dallas Cowboys.

Source: Sports Illustrated, “Inside the NFL: Powerball Numbers”, August 10, 1998.Suppose a sample of 18 new NFL players report their signing bonuses at the start of the 1998 season, and the results show a mean of $3.81 million and a standard deviation of $1.7 million. a. Estimate with 95% confidence the mean signing bonus based on the report. [Specify the

population parameter of interest, the criteria, the sample evidence, and the interval limits.]b. Discuss how this situation does or does not satisfy the assumptions for the inference.

2. Ten randomly selected shut-ins were each asked to list how many hours of television they watched per week. The results are

82 66 90 84 75 88 80 94 110 91Determine the 90% confidence interval estimate for the mean number of hours of television watched per week by shut-ins. Assume the number of hours is normally distributed.

3. The weights of the drained fruit found in 21 randomly selected cans of peaches packed by Sunny Fruit Cannery were (in ounces)

11.0 11.6 10.9 12.0 11.5 12.0 11.2 10.5 12.2 11.8 12.111.6 11.7 11.6 11.2 12.0 11.4 10.8 11.8 10.9 11.4

Using a computer or a calculator,a. Calculate the sample mean and standard deviation.b. Assume normality and construct the 98% confidence interval for the estimate of the mean

weight of drained peaches per can.

4. "Obesity raises heart-attack risk" according to a study published in the March 1990 issue of the New England Journal of Medicine. "Those about 15 to 25 percent above desirable weight had twice the heart disease rate." Suppose the data listed below are the percentages above desired weight for a sample of patients involved in a similar study.

18.3 19.7 22.1 19.2 17.5 12.7 22.0 17.2 21.1 16.2 15.419.9 21.5 19.8 22.5 16.5 13.0 22.1 27.7 17.9 22.2 19.718.1 22.4 17.3 13.3 22.1 16.3 21.9 16.9 15.4 19.3

Use a computer or calculator to test the null hypothesis, = 18%, versus the alternative hypothesis, 18%. Use = 0.05.

5. A telephone survey was conducted to estimate the proportion of households with a personal computer. Of the 350 households surveyed, 75 had a personal computer.a. Give a point estimate for the proportion in the population who have a personal computer.b. Give the maximum error of estimate with 95% confidence.

6. An article titled "Why Don't Women Buy CDs?" appeared in the September 1994 issue of Music magazine. Yehuda Shapiro, marketing director of Virgin Retail Europe, found that across Europe 40% of his customers who buy classical records are women. Determine a 90% confidence interval for the true value of p if the 40% estimate is based on 1000 randomly selected buyers.

7. "Parents should spank children when they think it is necessary, said 51% of adult respondents to a survey-though most child-development experts say spanking is not appropriate. The survey of 7225 adults . . . was co-sponsored by Working Mother magazine and Epcot Center at Walt Disney World." This statement appeared in the Rochester Democrat & Chronicle (12-20-90). Find the 99% confidence maximum error of estimate for the parameter p, P(should spank when necessary), for the adult population.

8. In a survey of 12,000 adults aged 19 to 74, National Cancer Institute researchers found that 9% in the survey ate at least the recommended two servings of fruit or juice and three servings of vegetables per day (Ladies Home Journal, April 1991). Use this information to determine a 95% confidence interval for the true proportion in the population who follow the recommendation.

9. a. Calculate the maximum error of estimate for p for the 95% confidence interval for each of the situations listed in the table.

Approximate Value of pSample Size n 0.1 0.3 0.5 0.7 0.9

100500

10001500

b. Explain the relationship between answers in columns 0.1 and 0.9; 0.3 and 0.7.

10. According to the June 1994 issue of Bicycling, only 16% of all bicyclists own helmets. You wish to conduct a survey in your city to determine what percent of the bicyclists own helmets. Use the national figure of 16% for your initial estimate of p.a. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.b. Find the sample size if you want your estimate to be within 0.04 with 90% confidence.c. Find the sample size if you want your estimate to be within 0.02 with 98% confidence.d. What effect does changing the maximum error have on the sample size? Explain.e. What effect does changing the level of confidence have on the sample size? Explain.

11. A bank believes that approximately 2/5 of its checking-account customers have used at least one other service provided by the bank within the last six months. How large a sample will be needed to estimate the true proportion to within 5% at the 98% level of confidence?

12. Paul Polger, a meteorologist with the National Weather Service, says that weathermen now accurately predict 82% of extreme weather events, up from 60% a decade ago. In fact, Polger claims, “We’re doing as well in a two-day forecast as we did in a one-day forecast twenty years ago.” Source: Life, “Predicting: Yesterday, Today. and Tomorrow”, August, 1998.You wish to conduct a study of extreme weather forecast accuracy by comparing local forecasts with actual weather conditions occurring in your city. a. What is the best estimate available for the probability of accuracy in predicting extreme

weather events.b. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.c. Find the sample size if you want your estimate to be within 0.04 with 95% confidence.d. Find the sample size if you want your estimate to be within 0.06 with 99% confidence.e. If the level of confidence remains constant, what happens to the required sample size if you

wish to double the maximum error of your estimate?

13. According to the May 1990 issue of Good Housekeeping, only about 14% of lung cancer patients survive for five years after diagnosis. Suppose you wanted to see if this survival rate were still true. How large a sample would you need to take to estimate the true proportion surviving for five years after diagnosis to within 1% with 95% confidence? (Use the 14% as the value of p.)

14. The article "Making Up for Lost Time" (U.S. News & World Report, July 30, 1990) reported that more than half of the country's workers aged 45 to 64 want to quit work before they reach age 65. Suppose you conduct a survey of 1000 randomly chosen workers in order to test Ho: p = 0.5 versus Ha: p < 0.5, where p represents the proportion who want to quit before they reach age 65. 460 of the 1000 sampled want to quit work before age 65. Use = 0.01.a. Calculate the value of the test statistic.b. Solve using the p-value approach. c. Solve using the classical approach.

15Many students work full-time or part-time. Listed below is the amount earned last month by each in a sample of 35 college students.

0 0 105 0 313 453 769 415 244 0 333 00 362 276 158 409 0 0 534 449 281 37 338

240 0 0 0 142 0 519 356 280 161 0

Use this sample data to describe the amount earned by working college students.a. How many of the students in the sample above are working?b. Describe the variable, amount earned by a working college student last month, using one

graph, one measure of central tendency, one measure of dispersion.c. Find evidence to show that the assumptions for use of Student's t-distribution have been

satisfied.d. Estimate the mean amount earned by a college student per month using a point estimate

and a 95% confidence interval.e. A Statistical Snapshot® suggests the average amount earned each month by college

students is approximately $350. Does the sample show sufficient reason to reject that claim?

16. Many U.S. housewives wouldn’t think of leaving home to go shopping without their stash of coupons, as reported in a 1998 issue of Family Circle. In fact, couponing has been a popular practice for over 30 years. The amount that people save at the supermarket by redeeming coupons varies substantially; some shoppers routinely save $50 or more per trip, whereas others save little if anything. Couponing has also been criticized for generating sales of frivolous products and overstocking of items that ordinarily would have remained on the shelf, and it takes longer to check out at the cash register. On the other hand, coupon queens tend to be more educated and living in higher-income households.

Source: Family Circle, “The Great Grocery Challenge”, September 15, 1998.Suppose the mean of all coupon sales at supermarkets in the U.S. is $10. A random sample of 25 shoppers with annual household incomes exceeding $75,000 is taken and reveals a mean redemption of $15 and a standard deviation of $7. Do shoppers from the higher-income group redeem coupons worth more than those redeemed by the rest of the nation? Use = 0.01.

17. Home schooling became legal in all 50 states in 1993, thus allowing parents to take charge of their kids’ education from kindergarten to college. Researchers estimate that as many as 1.5 million children and teenagers in 1998 were being taught primarily by their mothers and fathers; about five times as many as there were ten years earlier. This number is rather remarkable considering that the number of two-income households also rose during the same period. (i.e., Who’s staying at home teaching the kids?) The average ACT score for a home-schooled in 1998 was 23, whereas the average for traditionally schooled students was 21.

Source: Newsweek, “Learning at Home: Does it Pass the Test?”, October 5, 1998. Suppose a recent survey of 22 home schoolers in your state revealed a mean ACT score of 23.2 and a standard deviation of 4.1. Do the ACT scores of home schoolers in your state exceed the scores for the traditionally schooled? Use the 0.05 level of significance.

18. The LEXIS, a national law journal, found from a survey conducted on April 6-7, 1991, that nearly two-thirds of the 800 people surveyed said doctors should not be prosecuted for helping people with terminal illnesses commit suicide. The poll carries a margin of error of plus or minus 3.5%.a. Describe how this survey of 800 people fits the properties of a binomial experiment.

Specifically identify: n, a trial, success, p, and x.b. Exactly what is the "two-thirds" reported? How was it obtained? Is it a parameter or a

statistic?c. Calculate the 95% confidence maximum error of estimate for the population proportion of all

people who believe doctors should not be prosecuted.d. How is the maximum error, found in (c), related to the 3.5% mentioned in the survey report?

19. Prevention magazine reported in its latest survey that 64% of adult Americans, or 98 million people, were overweight. The telephone survey of 1254 randomly selected adults was conducted November 8-29, 1990, and had a margin of error of three percentage points.a. Calculate the maximum error of estimate for 0.95 confidence with p' = 0.64.b. How is the margin of error of three percentage points related to answer (a)?c. How large a sample would be needed to reduce the maximum error to 0.02 with 95%

confidence?

20. "Two of five Americans believe the country should rely on nuclear power more than other energy sources for energy in the 1990s, according to a poll released yesterday .The telephone poll, taken April 10 - 11, has a margin of error of plus or minus 3 points." This statement appeared in the Rochester Democrat & Chronicle on April 21, 1991. Forty percent plus or minus three points sounds like a confidence interval.a. What is another name for the "margin of error of plus or minus 3 points"?b. If we assume a 95% level of confidence, how large a sample is needed for a maximum error

of 0.03?

Chapter 10

1. When the Dow Jones industrial average dropped 512 points on August 31, 1998, it was the largest point drop since the 554-point drop that hit the stock market on October 27, 1987. Prior to that drop, some experts had predicted a 9,500 Dow before the end of the year, but after the August slide, opinions changed. The consensus by many analysts seemed to be that the market would not bounce back in time to even approach the level predicted by earlier estimates. The bull was tired. Source: Fortune, “Requiem for the Bull”, September 28, 1998.A random sample of 18 closing stock prices from the New York Stock Exchange was taken on August 25, 1998 (about one week prior to the “crash”), and again using the same stocks on September 15, 1998. Both dates are on a Tuesday. Results are shown in the table below:

Stock August 25 September 15 Stock August 25 September 151 10 ½ 11 10 7 ¾ 8 ½ 2 11 ¼ 9 11 14 ½ 13 ½ 3 23 ¾ 21 ¼ 12 16 ¼ 17 ¼ 4 14 11 ½ 13 65 ½ 63 ½5 12 ½ 7 ¼ 14 53 ¼ 56 ¼6 19 ¾ 18 ½ 15 43 ½ 41 ½7 27 ¼ 22 ½ 16 71 70 ¼8 32 24 ¼ 17 32 ½ 34 ½9 56 ½ 59 ¼ 18 17 ¼ 16 ½

a. On the basis of these data, construct a 90% confidence interval for the mean change from August 25 to September 15.

b. Can you conclude that the stock market was still suffering from the August 31 slide by September 15 or had it recovered? Explain.

2. An article titled, “Influencing Diet and Health Through Project LEAN” (Journal of Nutrition Education, July/August 1994) compared 28 individuals with borderline-high or high cholesterol levels before and after a nutrition education session. The participants’ cholesterol levels were significantly lowered, and the p-value was reported to be less than 0.001. A similar study involving 10 subjects was performed with the following cholesterol reading results:

Subject 1 2 3 4 5 6 7 8 9 10Presession 295 279 250 235 255 290 310 260 275 240Postsession 2665 266 245 240 230 230 235 250 250 215

Let d = presession cholesterol – postsession cholesterol.Test the null hypothesis that the mean difference equals zero versus the alternative that the mean difference is positive at = 0.05. Assume normality.a. Solve using the p-value approach. b. Solve using the classical approach.

3. The two independent samples shown in the following table were obtained in order to estimate the difference between the two population means. Construct the 98% confidence interval.

Sample A 6 7 7 6 6 5 6 8 5 4Sample B 7 2 4 3 3 5 4 6 4 2

4. An article titled "Stages of Change for Reducing Dietary Fat to 30% of Energy or Less" (Journal of the American Dietetic Association, Vol. 94, No. 10, October 1994) measured the energy from fat (expressed as a percent) for two different groups. Sample 1 was a random sample of 614 adults who responded to mailed questionnaires, and sample 2 was a convenience sample of 130 faculty, staff, and graduate students. The following table gives the percent of energy from fat for the two groups.

Group n Mean Standard Deviation 1 614 35.0 6.32 130 32.0 9.1

a. Construct the 95% confidence interval for 1 - 2.b. Do these samples satisfy the assumptions for this confidence interval? Explain.

5. A study was designed to compare the attitudes of two groups of nursing students toward computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction through the use of statistical packages. Group 2 had taken a statistical methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Index (CAIN). The results were as follows:

Group 1 (with computers): n = 10 = 60.3 s = 7.5Group 2 (without computers): n = 15 = 67.2 s = 2.1

Do the data show that the mean score for those with computer experience was significantly less than the mean score for those without computer experience? Use = 0.05.

6. A 1998 study of the Y2K problem investigated consumer opinions over what should be done to handle the situation and who should be responsible for monitoring the progress. In response to the question, “Who should monitor the report on progress in solving the Y2K problem?”, 34% of the respondents surveyed felt that it was the government’s responsibility.

Source: Newsweek, “It’s Not My Problem”, October 5, 1998.

Suppose you believe that differences in opinion exist between rural and city dwellers on whether the government should monitor the Y2K problem. A study of 250 heads of households in the city and 200 rural heads of households are asked the above question. You find that 100 of the city dwellers and 64 of the rural dwellers believed that it was the government’s responsibility. Is there a significant difference in the opinions of the two groups? Use = 0.05.

7. One of the most commonly seen applications of statistics is the poll percentages, reported in the news, of people who say, think or do some specific thing. So who does “know the American flag?” Two hundred adults in Erie County, NY were asked how many stars there are on the USA flag. The table below shows the number of adults belonging to each category. The sample results were tallied twice, by gender and by residence of adult answering question.

Men Women City Urban Ruraln(Knew) 72 72 57 58 31n(Didn’t know) 22 34 25 14 15

a. Is there a significant difference between the percentage of men and the percentage of women who answered the question correctly? Use = 0.05.

b. Is there a difference between the percentage of city and the percentage of urban adults who answered the question correctly? Use = 0.05.

8. Twelve automobiles were selected at random to test two new mixtures of unleaded gasoline. Each car was given a measured allotment of the first mixture, x, and driven; then the distance traveled was recorded. The second mixture, y, was immediately tested in the same manner. The order in which the x and y mixtures were tested was also randomly assigned. The results are given in the following table.

CarMixture 1 2 3 4 5 6 7 8 9 10 11 12

x 7.9 5.6 9.2 6.7 8.1 7.3 8.1 5.4 6.9 6.1 7.1 8.1y 7.7 6.1 8.9 7.1 7.9 6.7 8.2 5.0 6.2 5.7 6.2 7.5

Can you conclude that there is no real difference in mileage obtained by these two gasoline mixtures at the 0.10 level of significance? Assume mileage is normal.a. Solve using the p-value approach. b. Solve using the classical approach.

9. The following data were collected concerning waist sizes of men and women. Do these data present sufficient evidence to conclude that men have larger mean waist sizes than women at the 0.05 level of significance? Assume waist sizes are normally distributed.

Men 33 33 30 34 34 40 35 35 32 34 32 35 32 32 34 36 30 38

Women 22 29 27 24 28 28 27 26 27 26 25

Chapter 11

1. A nationwide survey of consumers in 1998 was conducted to determine the level of uncertainty surrounding the Y2K problem. CIO Communications, Inc. asked heads of households, “What are you planning to do with your money if the Y2K problem isn’t solved by mid-1999?” The results are shown in the table below:

Plans for Money (National) Percent RespondingHide it (mattress stuffing) 25Deposit it in several banks 11Deposit it in one bank 16Don’t know 48

Total 100

Source: Newsweek, “Don’t Bank on It”, August 24, 1998, p. 9.

Suppose a local follow-up survey is conducted using 300 respondents from your city who answer exactly the same question. Results from the follow-up study are tabulated below:

Plans for Money (Local) Number RespondingHide it (mattress stuffing) 72Deposit it in several banks 32Deposit it in one bank 47Don’t know 149

Total 300

Does the distribution of responses differ from the distribution obtained from the nationwide survey? Test at the 0.05 level of significance.a. Solve using the p-value approach. b. Solve using the classical approach.

2. An article titled "Human Papillomavirus Infection and Its Relationship to Recent and Distant Sexual Partners" (Obstetrics & Gynecology, November 1994) gave the following results concerning age and the percent who were HPV-positive among the 290 participants in the study.

Age N HPV-Positive (%) 20 27 40.721-25 81 37.026-30 108 31.531-35 74 24 .3

Complete the test of the hypothesis that the same proportion of each age group is HPV-positive for the population this sample represents. Use 05.a. Solve using the p-value approach. b. Solve using the classical approach.

ple show that the median score for the exam is less than 50? Use = 0.05.