Ch-1 Introduction and Data Collection

Business decisions may be made by interpreting a statistical analysis of the variables of the process associated with the decision or by using instinct and insight derived from experience with the business process. When might a decision be made by these latter more "unstructured" techniques?

Instinct is part of statistics.

Instinct or insight is always used in decision-making.

Variables associated with the business process cannot be measured.

The business process on which the decision is made is unknown.

Which of the following exhibits the correct relationship between variables and values?

Color of an automobile; $23,000.

Red; price of an automobile.

Color of an automobile; price of an automobile.

Red; $23,000.

A statistics professor surveys the students in her class and finds that 20% are sophomores and 45% are juniors. This is an example of:

nominal data.

inferential statistics.

secondary data.

descriptive statistics.

What statistical task performed by the U.S. government led to the development of computers?

determining import tariffs

evaluating the national budget

analyzing the census results

calculating income taxes

Which of the following does not represent one method to obtain primary source data?

Looking in professional magazines

Making observations

Conducting an experiment

Sending a survey to customers

The grades that a random sample of MBA students received over the last five years of International Business classes represent what statistical concept?

The grades are a parameter.

The grades are a population.

The grades are a sample.

The grades are a statistic.

What method is used to sample a population so that it is representative of the population?

Samples are chosen at random from the population.

All but the observations that have the lowest and highest values are selected.

Only the first half of a population is selected.

Every other element in a population is chosen.

A newspaper advertising sales representative earns a commission on each advertisement sold. This person made $3,000 in commissions during one month and concludes that annual compensation will be $36,000. This is an example of:

inferential statistics.

secondary data.

descriptive statistics.

nominal data.

A consumer confidence researcher asks several retailers to report the number of LCD televisions sold during a particular month. These numbers most likely represent what level of measurement?

ordinal

interval

nominal

ratio

A student evaluation of teaching effectiveness for a particular course asks students to respond to their level of agreement with several statements according to the scale 1 = Strongly Agree, 2 = Agree, 3 = Neutral, 4 = Disagree, and 5 = Strongly Disagree. The responses indicate what level of measurement?

ratio

ordinal

nominal

interval

A company publishes data on its quarterly earnings for its stockholders to evaluate. Is this data primary or secondary source data?

The source is secondary for the company and primary for the stockholders.

The source is primary for the company and secondary for the stockholders.

The source is secondary for both the company and the stockholders.

The source is primary for both the company and the stockholders.

If you have a digital scale in your home that only reads in integers, is your weight a discrete variable?

No because weight is still a continuous variable regardless of the ability to measure it.

Yes because the scale reports integers.

It depends on your weight.

It depends on the accuracy of the scale.

Look at the survey questions that Good Tunes sent to their customers. What type of variable and levels of measurement do the questions concerning overall service, selection, and quality of the items purchased represent?

Categorical variables measured on an ordinal scale.

Continuous variables measured on a ratio scale.

Categorical variables measured on the nominal scale.

Categorical variables measured on the interval scale.

A question on a product registration card asks, How much money do you plan to spend on DVD movie purchases during the next 6 months? What type of variable and level of measurement does your response represent?

Continuous variable measured on a ratio scale.

Discrete variable measured on a nominal scale.

Discrete variable measured on an ordinal scale.

Continuous variable measured on an interval scale.

How might you obtain a statistic, that is a numerical value, from a categorical variable that has "Yes" or "No" as the only possible responses?

You could count the number of "Yes" and "No" responses in the sample.

You could count the number of possible responses (two).

You cannot obtain a numerical value from a categorical variable.

At best you could only obtain an ordinal measure or ranking of the responses if you count one response over the other.

Ch-2 Presenting Data in Tables and Charts

What is the purpose of a summary table?

To see differences between or among categories.

This is the only way to present categorical data in numerical form.

To list data to create a bar or pie chart.

To sum the values of responses to a survey.

A graphical representation of a frequency distribution is called a__________________ .

histogram

stem-and-leaf plot

time-series plot

scatter diagram

You have a summary table and a simple bar chart (like the ones at the beginning of the chapter) indicating where customers prefer to do their banking. How could you enhance the bar chart to provide both visual and actual information?

Only the summary table can show the actual values for the data.

Add values to the bar chart like what is commonly done on a pie chart.

The bar chart and summary table must be presented together in order to represent this data.

Use vertical lines on the bar chart to show the values more precisely.

It might be said that the stem-and-leaf display is really a quick and easy way of creating a rudimentary chart or diagram for numerical data. If so, which chart is used to describe categorical data does it most closely resemble?

The stem-and-leaf display most closely resembles a rudimentary bar chart.

The stem-and-leaf display most closely resembles a rudimentary pie chart.

The stem-and-leaf display most closely resembles a rudimentary Pareto chart.

The stem-and-leaf display does not resemble any of the above charts or diagrams.

The width of a class interval in a frequency distribution (or bar chart) will be approximately equal to the range of the data divided by the ______________ .

highest value in the data set

number of class intervals

lowest value in the data set

average of the data set

Which of the above histograms represents the graph of city restaurant meal prices with an interval of $8?

Only the histogram on the left

Neither histogram

Only the histogram on the right

Both histograms

When constructing a frequency distribution, which of the following rules must be followed?

The number of classes must be an even number.

The width of each class is equal to the lowest value in the data set.

Adjacent classes cannot overlap.

The midpoint of each class must be an integer.

The rule of thumb for creating a frequency distribution is to divide the data into 5-15 classes. While larger numbers of classes allow for larger data sets, how do you know exactly how many classes to use?

If in doubt about the number of classes, select 10 since it is the midpoint between 5 and 15 classes.

Select the number of classes that provides definition to the shape of the data.

Determine the width of the class interval, then calculate the number of classes.

Any number of classes between 5 and 15 is sufficient.

The following numbers represent exam scores in an accounting class: 78, 93, 85, 81, 73, 96, 72, 86, 90, 85 If a stem-and-leaf diagram is developed from this data, how many stems will be used?

3

4

10

5

In the above figure of wine imports into the United States, what three guidelines for developing good graphs have not been followed?

Distorted data, unnecessary adornment, no scales for either axis.

Unnecessary adornment, vertical scale does not begin at zero, no title.

Distorted data, unnecessary adornments, vertical axis not properly labeled.

Distorted data, X axis not labeled, no title.

Considering the various types of tables and charts introduced in this chapter, which table, chart, diagram or plot would you use to depict categorical data for two variables in a visual format?

contingency table

pie chart

scatter plot

side-by-side bar chart

The cumulative frequency for a particular class is equal to 35. The cumulative frequency for the next class will be _________________ .

less than 35.

35 plus the next class frequency.

35 minus the next class frequency.

equal to 65.

Which of the following would be most helpful in the construction of a pie chart?

frequency distribution

cumulative percentages

relative frequencies

ogive

The table above shows the frequency and relative frequencies for 7 groups of restaurant meal prices. How was the value of 0.36 obtained for the relative frequency of meals costing $32 but less than $40?

The number of data points is 50, so divide 18 by 50.

(18 x 2)/100 = 0.36.

The midpoint of the class is $36, so divide 36 by 100.

(18/100) x 2 = 0.36.

The highest bar in a histogram represents?

The class with the highest cumulative frequency.

The class with the highest frequency.

The class with the lowest frequency.

The class with the lowest relative frequency.

Ch-3 Numerical Descriptive Measures

How might an extreme value in the sample data set affect the value of the mean?

Since all values are summed, any extreme value can influence the mean to a large extent.

All values are treated equally when determining the mean, so an extreme value cannot affect it.

One extreme value is still only one value, so it cannot affect the mean very much.

An extreme value cannot affect the mean if it is close to the mean.

Which of the following is not a measure of central tendency?

Median

Mode

Interquartile range

Geometric mean

Which of the following is the most appropriate measure of central tendency for ordinal data?

Variance

Coefficient of Variation

Mean

Median

Which of the following measures of central tendency is not affected by extreme values in the sample data set?

Mean

Mode

Median and Mode

Median

How many elements of a data set are between the first and third quartiles?

One fourth

One third

One half

Three fourths

Which of the following measures become larger as the data is more dispersed?

Range, Variance, and Standard Deviation

Mean, Variance, and Standard Deviation

Mean and Median

Median and Range

The sum of deviations about the arithmetic mean is always equal to ______________ .

Variance

1

Geometric Mean

0

The Chebyshev Rule indicates that the percentage of values that will be found within three standard deviations of the mean will be _________ .

At least 97%

At least 75%

At least 67%

At least 89%

The distribution above is:

symmetric

skewed to the left

skewed to the right

normally distributed

Which of the following is not required for the construction of a boxplot?

Second quartile

Largest value

Mean

Median

A numerical measure for the strength of the linear relationship between two variables is?

Sample standard deviation

Sample linearity

Sample dispersion

Sample covariance

The coefficient of correlation will be a value in which of the following ranges?

(-infinity, +infinity)

(-1, 1)

(-1, 0)

(0, 1)

How is the arithmetic mean related to the variance?

Variance is not related to the mean, but standard deviation is.

Variance has the square of the mean in its formula.

Variance measures the variability of values about the mean.

They are not related. One is a measure of central tendency, and the other is a measure of variance.

When computing numerical descriptive measures from values that have been summarized by a frequency distribution, which of the following is most important to the calculation?

The midpoint of the class intervals.

The range of the frequency distribution.

The standard deviation of the class intervals.

The number of class intervals in the frequency distribution.

The difference between a data value and the arithmetic mean of a sample divided by its standard deviation is called:

the empirical rule

Coefficient of correlation

Mean variation

Z score

Ch-4 Basic ProbabilityYou observe 1000 leaves falling from a tree and record whether they land with their top or bottom showing and find that 583 or 58.3% land with their bottom showing. What approach to probability does this represent?

Subjective probability

Empirical probability

A priori probability

None of the above; this is just a math problem.

Instead of observing the falling leaves as in Question #1, you analyze a number of leaves and how they fall and predict that about 60% of the leaves will land with their bottom showing. What approach to probability does this represent?

Subjective probability

A priori probability

Empirical probability

None of the above; this is just a physics problem.

In the previous questions, if you are trying to determine whether a leaf will fall with its bottom side showing (event A), what is the collection of events that are not A called, including leaves landing with the tops showing, leaves landing on their sides, and any other possible outcomes?

Complement of event A

Sample space

Event B

Joint events

The General Addition Rule is used to determine the probability of either event A or event B occurring and states P(A or B) = P(A) + P(B) P(A and B). Why is P(A and B) subtracted?

There is no explanation other than its just a part of the theory.

P(A and B) has been counted twice through P(A) and P(B).

This rule determines the probability of event A or B occurring, not A and B, so this factor is subtracted.

You do not have to subtract P(A and B) if A and B are statistically independent.

Which of the following is not a valid probability value?

4/3

11/13

0

0.57

If an event is in set R but is not in set S, which of the following statements is true?

The event is in the union of R and S.

The event is in both the union and intersection of R and S.

The event is in the intersection of R and S.

The event is not in the union of R and S.

An investment advisor currently maintains a list of 15 recommended stocks. If a particular client would like to invest in 5 stocks, how many possible portfolios exist?

3003

75

360,360

15,015

A group of 7 MBA students has formed a team for a business competition. They must elect a project manager and a treasurer. In how many ways can these two officers be elected?

14

21

35

42

The table below provides information about the students in an accounting class:

If a student is selected at random from the class, what is the probability that the student is a male or a senior?

0.745

0.471

0.588

0.882

The table below provides information about the students in an accounting class:

A student is randomly selected from the class. Given that the student is female, determine the probability that the student is also a senior.

0.222

0.118

0.647

0.412

The table below provides information about the students in an accounting class:

A student is randomly selected from the class. Determine the probability that the student is a female if it is known that the student is a senior.

0.529

0.222

0.275

0.118

If events B and C are independent, which of the following is not true?

P(B or C) = P(B) + P(C) P(B)P(C)

P(B and C) = P(C)P(B)

P(B | C) = P(C)

P(C | B) = P(C)

Let E be the event that you roll an even number on a toss of a single die. Which of the following is not true?

P(E or E) = 1

P(E) = P(E) = 0.5

E = {1, 3, 5}

P(E and E) = 1

Bayes Theorem is used in which of the following situations?

When new information can be used to eliminate an event from consideration.

When multiple events are independent.

When multiple events are mutually exclusive.

When new information can be used to revise previously determined probabilities.

Abigayle, Brenda, and Charlie take orders at a fast-food restaurant. Abigayle Abigayle processes 35% of the orders, Brenda takes 25%, and Charlie does the remainder. Each of the employees will make an occasional error when entering orders into the terminal. Abigayle has 2% errors, Brenda makes an error 0.5% of the time, and Charlies error rate is 1%. Given that a mistake was made on the order, the manager wants to know the probability that Charlie was the one who entered the order. Which of the following concepts will not be used in your analysis?

Events that are collectively exhaustive

Events that are statistically independent

Bayes Theorem

Events that are mutually exclusive

Ch-5 Some important Discrete Probability Distributions

What value is the sum of the probabilities in a binomial distribution?

It varies with the number of values in the distribution.

It varies with the number of terms in the sum.

0

1

A particular game of chance has three possible outcomes (win, lose, and draw) with associated probabilities and monetary payouts given in the following table:

What is the expected value of the monetary winnings (loss) from playing the game?

$5

$0

$25

-$5

A particular game of chance has three possible outcomes (win, lose, and draw) with associated probabilities and monetary payouts given in the following table:

What is the standard deviation of the monetary winnings (loss) from playing the game?

$2500

$13,000

$50

$5

A binomial distribution has exactly how many possible outcomes?

It depends on the problem.

6

2

1

A manufacturing process produces defective items 5% of the time. A sample of 20 items is taken for quality control. If you wanted to determine the probability that exactly 2 of the 20 items are defective, which distribution should be used?

Hypergeometric

Binomial

Poisson

Continuous

A student randomly guesses on a multiple choice exam that has 15 questions with 4 options for each question. What is the probability that the student gets exactly 7 questions correct?

0.60

0.47

0.04

0.28

The Poisson distribution is to quantify the probability associated with a certain number of outcomes in which of the following?

1-p failures

some interval of time

n trials when sampling is done without replacement

n trials when sampling is done with replacement

Trains pass an intersection at the rate of 4 per day. What is the probability that exactly 5 trains will pass the intersection tomorrow?

0.175

0

0.781

0.156

The hypergeometric distribution is similar to a binomial distribution except?

There are more than two possible outcomes in the hypergeometric.

Sampling is done with replacement in the hypergeometric.

The number of trials is larger in the hypergeometric.

The probability of failure is 1-p.

A case of 15 compact fluorescent light bulbs is known to have 2 that are defective. If a sample of 4 light bulbs is selected, what is the probability that exactly 1 will be defective?

0.58

0.42

0.14

0.84

Fifty households in a particular neighborhood will file state income tax returns, and 5 will be fraudulent. If the state revenue commissioner selects 10 tax returns for detailed auditing, the number of fraudulent returns detected will follow what type of distribution?

Poisson

Binomial

Hypergeometric

Normal

Which of the following relationships regarding the expected value and variance of random variables is incorrect?

S(X + Y) = S(X) + S(Y)

Var(X + Y) = Var(X) + Var(Y) + 2Cov(XY)

E(X + Y) = E(X) + E(Y)

E(P) = wE(X) + (1-w)E(Y)

The number of people arriving to a movie theater in a 30-minute time period is best modeled using which of the following distributions?

Binomial

Normal

Poisson

Hypergeometric

A young investor has selected two mutual funds, growth and income. The growth fund has an expected return of $4,000 and variance of 60,000 while the income fund has an expected return of $2,500 with a variance of 45,000. If the growth fund is 70% of the portfolio, determine the expected return of the portfolio.

$3,000

$3,500

$3,750

$3,250

A young investor has selected two mutual funds, growth and income. The growth fund has an expected return of $4,000 and variance of 60,000 while the income fund has an expected return of $2,500 with a variance of 45,000. The covariance between the two mutual funds is 20,000. If the growth fund is 70% of the portfolio, determine the portfolio risk.

$325

$200

$185

$250

Ch-6 The Normal distribution and other Continous Distributions

Which of the following characteristics do normal and uniform distributions have in common?

The mean is equal to the median and the range is infinite.

The distributions are symmetric and all values are equally likely.

The distributions are symmetric and the range is infinite.

The distributions are symmetric and the mean is equal to the median.

The figure below represents which of the following distributions?

Negative Exponential

Uniform

Exponential

Normal

If x is uniformly distributed from 5 to 12, (5 x 12), determine the standard deviation of this distribution.

2

7

12

4

The area to the right of the mean in a normal distribution is indicated by which of the following?

the variance of the distribution

0.5

the standard deviation of the distribution

1

A standard normal distribution has which of the following properties?

The mean is equal to 0 and the variance is equal to 1.

The mean and the variance both equal 1.

The mean is equal to the standard deviation.

The mean is equal to the variance.

Let z be a normal random variable with a mean of 0 and a standard deviation of 1. Determine P(z 1.4).

0.0808

0.9192

0.4192

0 because P(z = 1.4) = 0.

Let x be a normal random variable with a mean of 50 and a standard deviation of 3. A z score was calculated for x, and the z score is -1.2. What is the value of x?

53.6

0.1151

0.8849

46.4

Let x be a normal random variable with a mean of 35 and a standard deviation of 4. Determine P(30 x 37).

0.1056

0.2971

0.6915

0.5859

What percentage of a normal distribution is found within a range of z scores from -2 to +2?

99%

90%

85%

95%

Suppose you are working with a data set that is normally distributed with a mean of 70 and a standard deviation of 10. Determine the value of x such that 65% of the values are greater than x.

60

80

66

74

In which of the following continuous distributions are extreme values most likely (within its range)?

Extreme values are rare for all continuous distributions

Exponential

Uniform

Normal

On the day before an exam in an online class, students email questions to the professor at a rate of 1 every 20 minutes, exponentially distributed. Determine the probability that more than 1 hour elapses between email messages.

37%

5%

95%

63%

For an exponential distribution with the parameter lambda equal to 10 per minute, what is the mean of the exponential distribution?

0

0.17

cannot be determined from the given information

0.1

Let x be a binomial random variable with n = 30 and p = 0.7. Using the normal distribution to approximate the binomial, to determine the probability of more than 16 but less than 25 successes, which of the following is the correct representation?

P(17 < x < 24)

P(16.5 < x < 24.5)

P(17.5 < x < 24.5)

P(16 < x < 25)

Let x be a binomial random variable with n = 25 and p = 0.6. Using the normal distribution to approximate the binomial, determine the probability that more than 12 successes will occur.

0.0808

0.8461

0.9192

0.1539

Ch-7 Sampling and Sampling Distributions

Ten samples of 20 boxes of cereal are weighed, and the means of the samples are found to vary from 364.4 to 371.9 grams. If ten more samples of 30 boxes each were weighted, which of the following ranges of means would you most likely expect to find among the ten samples, given =368 grams and s=15 grams?

364.4371.9

366.4369.1

368368

365.3370.7

Why use samples rather than the entire population?

Selecting a sample is less time-consuming than using every item in the population.

An analysis based on a sample is more practical than an analysis of the population.

Selecting a sample is less costly than using every item in the population.

All of the above reasons justify statistical sampling procedures.

During the last general election, 70% of registered voters actually voted. What is the probability that a telephone survey of 20 registered voters will indicate that less than half actually voted?

0.0251

0.0202

The survey of 20 voters is not a large enough sample

0.9745

Which of the following sampling techniques will not result in a probability sample?

stratified

random

quota

systematic

A human resources department processes reimbursement requests for travel expenses. Three hundred completed forms were submitted in the past month, and in order to estimate the average travel expense, the HR Director constructs a sampling procedure that will begin with the 7th expense form and collect every 10th form thereafter (17th, 27th, etc.). This procedure results in which of the following types of samples?

systematic

simple random

convenience

stratified

The standard deviation of a sampling distribution is commonly called which of the following?

standard error

standard margin

sampling deviation

statistical range

The Central Limit Theorem states that if n is large enough the distribution of sample means follows which distribution?

random

exponential

normal

uniform

Ten samples of 30 boxes of cereal are weighed, and the means of the samples are found to vary from 365.3 to 370.7 grams. What is the probability that another sample of 30 boxes will have a mean of less than 365.3 grams?

0.8379

0.5

0.1621

0.4863

Increasing the sample size causes the standard error of the proportion to:

remain the same

become less normal

increase

decrease

Ten samples of 30 boxes of cereal are weighed, and the means of the samples are found to vary from 365.3 to 370.7 grams. What is the interval around the population mean that is expected to contain 75% of the sample means?

366.1369.9

365.3370.7

367.4368.6

364.9371.2

Which of the following situations would most likely be an example of an unethical sampling method rather than just an inaccurate one?

Sampling only people who shop from 5-6 PM at a store to determine how many people are buying a sale item.

Sampling only certain neighborhoods in a town to determine how to spend tax money on a recreation project.

Sampling only the people who go through a particular entrance to determine which team the spectators hope will win the game.

Sampling only those who answer the phone when you call them to determine which TV programs are watched in a particular city.

If a population has a mean of 350 and a standard deviation of 25, determine the probability that a random sample of 40 will have a mean between 335 and 375.

0.7257

0.2743

0.8413

0.5670

Suppose that 65% of all college students have an iPod. What is the probability that a sample of 50 will indicate that more than 30 students own an iPod?

0.2296

0.7704

0.2704

0.60

Forty percent of teens prefer a new video game package to the existing design. If the marketing department conducts a survey of 200 teens, what is the probability that the random sample will indicate a sample proportion greater than 50%?

0.0019

0.50

0.9981

0.4981

Which of the following is not a potential survey error?

measurement

nonresponse

coverage

judgment