CHAPTER 16

Chapter 16: Generalizing a Samples Findings to Its Population and Testing Hypotheses about Percents and Means

CHAPTER 16GENERALIZING A SAMPLES FINDINGS TO ITS POPULATION AND TESTING HYPOTHESES ABOUT PERCENTS AND MEANS

LEARNING OBJECTIVES

To distinguish statistics from parameters

To understand the concept of statistical inference

To learn how to estimate a population mean or percentage

To test a hypothesis about a population mean or percentage

To learn how to perform and interpret statistical inference with SPSS

CHAPTER OUTLINE

Sample Statistics and Population Parameters

The Concepts of Inference and Statistical InferenceParameter Estimation

Sample Statistic

Standard Error

Confidence Intervals

How to Interpret an Estimated Population Mean or Percentage RangeTHE HOBBITS CHOICE SURVEY: How To Obtain A Confidence Interval For A Percentage With SPSS

THE HOBBITS CHOICE SURVEY: How To Obtain A Confidence Interval For A Mean With SPSS

HYPOTHESIS TESTS

Test of the Hypothesized Population Parameter Value

Directional Hypotheses

How to Interpret Hypothesis Testing

How to Use SPSS to Test a Hypothesis for a Percent

How to Use SPSS to Test a Hypothesis for a Mean

KEY TERMS

Statistics

Parameters

Inference

Statistical inference

Parameter estimation

Hypothesis test

Tests of significant differences

Standard error

Standard error of a mean

Standard error of a percentage

Confidence intervals

Most commonly used level of confidence

Formula for population parameter estimation

Hypothesis

Hypothesis testing

Intuitive hypothesis testing

Hypothesized population parameter

Alternative hypothesis

Sampling distribution concept

Directional hypothesis

TEACHING SUGGESTIONS1. A way to tie concepts in different chapters together is to remind students of the sample size-sample accuracy relationship that is depicted on the graph in chapter 13. This graph was used to introduce the relationship of a samples (statistical) accuracy and its size. In chapter 16, the sample has been gathered, and the statistics such as mean and percent findings have been calculated. Chapter 16 brings the sample accuracy concept full circle as the accuracy level is now being used to determine estimates of the population parameters.

2. The effect of sample size on a confidence interval can be demonstrated with a simple spreadsheet program such as Excel or Lotus 1-2-3. Lets assume that p has been found to be 40%, what would be the confidence intervals under successively larger sample sizes? The following table is a spreadsheet-like comparison for 95% confidence intervals.

Sample SizeLower LimitUpper LimitRange

10030.4%49.6%19.2%

25033.9%46.1%12.1%

50035.7%44.3%8.6%

100037.0%43.0%6.1%

150037.5%42.5%5.0%

200037.9%42.1%4.3%

3. The effect of variability in the sample statistic can be illustrated in the same way. Lets hold the sample size at 250, and compare different sizes of p.

Statistic (p)Lower LimitUpper LimitRange

5043.8%56.2%12.4%

4033.9%46.1%12.1%

3024.3%35.7%11.4%

2015.0%25.0%9.9%

106.3%13.7%7.4%

52.3%7.7%5.4%

4. Because SPSS combines a mean confidence interval and a mean hypothesis test in its One Sample t Test procedure, students may become confused with the mean difference and 95% Confidence Interval of the Difference information provided by SPSS when testing a hypothesized mean. (That is, when the Test Value is set for any number other than the default zero.) It may be necessary to emphasize that these are of no practical value when performing a mean hypothesis test with SPSS.

5. Some textbooks, particularly statistics textbooks, explicitly state the alternative hypothesis. We do not do so in our textbook, but we have included a Marketing Research Insight on What Is an Alternative Hypothesis? Instructors who believe students should understand the concept of an alternative hypothesis may wish to emphasize this MRI or otherwise add material of their own on the concept of an alternative hypothesis.

6. With SPSS for Windows available to them, student may not appreciate doing hand calculations of confidence intervals or hypothesis tests. These calculations are more than tedious exercises. The point to them is to have students see what is in the numerator and what is in the denominator of each formula, so they can understand what is driving the computed value. Typically, the sample size is always in the denominator, while the hypothesized value and sample statistic are in the numerator. Larger sample sizes drive the computed value (e.g., a t-value) down; whereas, larger differences between the sample statistic and the hypothesized value will drive it up.

7. There are a few, but not many, hand calculation end-of-chapter questions. It may be beneficial to devote part of a class to in-class exercises where students calculate confidence intervals or test hypotheses using the end-of-chapter questions or questions generated by the instructor. Ask students to bring their hand calculators. Having each student work independently in a class setting and providing the step-by-step calculations will force students to use the formulas correctly.

8. This chapter is the first encounter for students with SPSS statistical test output. The text describes each output example in some detail and provides annotated output pages; however, much information is contained in each case, and students can become confused. It is recommended that instructors use overhead transparencies or other visual aids and review the relevant aspects of each output page during class time. Student should be oriented on where to find vital information such as mean, sample size, test statistic, and significance. Also, they should be instructed on how to interpret the findings.

9. Using an SPSS data set other than those provided in the text can be beneficial and a good test of how well students can adapt their learning to a new situation. Sources of these data sets can be: consulting data, prior semester student team research projects, or simulated data sets.

ACTIVE LEARNING EXERCISES

Calculate some Confidence IntervalsThis exercise provides students with experience in calculating confidence intervals for percentages and for a mean. In all cases, the sample size is 1,000, and they are to use the formulas provided in the chapter.

Formula for population parameter

Estimation (Mean)

Where

= sample mean

= z value for 95% or 99% level of confidence

= standard error of the mean

Formula for population parameter

Estimation (Percentage)

Where

p = sample percentage

= z value for 95% or 99% level of confidence

= standard error of the percentage

QuestionSample Statistic(s)95% Confidence Interval

Lower boundaryUpper boundary

Have you heard of satellite radio?50% responded yes

If yes, do you own a satellite radio?30% responded yes

If you own satellite radio, about how many minutes of satellite radio did you listen to last week?Average of 100.7 minutes; standard deviation of 25.0 minutes

Use SPSS for a Confidence Interval for a Mean

This exercise requires students to use the entire sample for the Hobbits Choice Restaurant survey data set and to have SPSS compute the confidence interval.

How does this confidence interval compare to the one we found for the likely patrons on the Hobbits Choice Restaurant? Compared to a 95% confidence interval of $266.99 to $296.92, the discovered one is much lower due to a lower mean and narrower due to the larger sample size.

Use SPSS for a Hypothesis Test for a Mean

Students will find that there is support for the hypothesis of $18 using the full sample. The SPSS output is below.

ANSWERS TO END-OF-CHAPTER QUESTIONS1. What essential factors are taken into consideration when statistical inference takes place?

Review question. Students will need to identify the factors noted in the discussion and formulas.

Statistical inference is a set of procedures where the sample size and sample statistics are used to make estimates of population parameters. The key factors taken into consideration are the sample size, the sample statistic, and the variability found in the sample. The sample size and variability are used to estimate the amount of sampling error.

2. What is meant by parameter estimation, and what function does it perform for a researcher?Review question. This question requires students to distinguish parameters from statistics and to relate how parameter estimation operates.

Parameter estimation is used to estimate the population value (parameter) through the use of confidence intervals. It is the process of using sample information to compute an interval that describes the range of a parameter such as the population mean () or the population percentage (). It involves the use of three values: (1) the sample statistic (such as the mean or the percentage), (2) the standard error of the statistic, and (3) the desired level of confidence (usually 95% or 99%). Parameter estimation serves the purpose of translating the sample statistic into a statement about the populations true value.

3. How does parameter estimation for a mean differ from that for a percentage?Review question. Students will need to distinguish between the two.

The major difference is in the computation of the standard error. With a mean, the standard deviation is used as a measure of the variability, while with a percentage; the variability is measured by the quantity (pq). Also, means are used for metric-scaled variables, while percentages are used for categorical variables.

4. List the steps in statistical hypothesis testing. List the steps in intuitive hypothesis testing. How are they similar? How are they different?Review question. This question requires students to find and list the steps in each one, and to identify where they are similar and where they differ.

The two types of hypothesis tests are listed and contrasted following. As can be seen, the intuitive approach does not rely on a random sample, nor is a sample statistic computed. The steps are very similar in order and nature, but intuitive hypothesis testing takes place without formal concern for the representativeness of the evidence and without a statistical test.

Statistical Hypothesis StepsIntuitive Hypothesis Steps

Step 1. Begin with a statement about what you believe exists in the population; that is, the population mean or percentage.

Believe something.

Step 2. Draw a random sample and determine the sample statistic.

Find some evidence that about your belief.

Step 3. Compare the statistic to the hypothesized parameter.

Compare the evidence to your belief.

Step 4. Decide whether the sample supports the original hypothesis. The evidence agrees or does not agree with your belief.

Step 5. If the sample does not support the hypothesis, revise the hypothesis to be consistent with the samples statistic. Find something that disagrees with your belief, and now believe something different.

5. When a researchers sample evidence disagrees with a managers hypothesis, who is right?Review question. In order to answer this question, students must grasp the fact that the researcher uses random samples that are truthful (valid) representations of the population under study.

Sample information and what it infers about the hypothesis by application of proper hypothesizing testing procedures is always more accurate than the hypothesis. This claim, of course, assumes that nonsampling errors are inconsequential, and a random (i.e., representative) sample has been drawn.

6. What does it mean when a researcher says that a hypothesis has been supported at the 95% confidence level?Review question. Students must demonstrate a basic understanding of a sampling distribution.

It means that the sample finding (statistic and variability) is such that the statistic falls in the interval describing 95% of the sampling distribution. The sample and its statistic are but one of many, many theoretical samples making up the sampling distribution that has the hypothesized population value as the center of the sampling distribution.

7. Distinguish a directional from a nondirectional hypothesis and provide an example of each one.Review question. Students will need to show an understanding of these two types of hypothesis tests.

A directional hypothesis is one that indicates the direction in which you believe the population parameter to fall. There are two things to keep in mind for directional hypothesis tests. First you must be concerned with the sign determined for the Z value as well as its size. With greater than hypotheses, the sign must be positive, while for less than hypotheses, the sign must be negative, when you subtract the hypothesized mean from the sample mean. Second, although we are working with only one side of the bell-shaped distribution, you need to adjust the critical z value (refer to Table 16.5). The directional hypothesis is supported at that level of confidence if the computed z is larger than the critical cut point, and, of course, its sign is consistent with the direction of the hypothesis. Otherwise, the directional hypothesis is not supported at your chosen level of confidence. (Students should illustrate with an example.)

8. Here are several computation practice exercises to help you identify which formulas pertain and learn how to perform the necessary calculations. In each case, perform the necessary calculations and write your answers in the column identified by a question mark.

a. Determine confidence intervals for each of the following:

Mean of 150, s.d. of 30, n of 200, level of 95% - Use mean equation

Percent of 67%, n of 300, level of 99% - Use percentage formula

Mean of 5.4, s.d. of 0.5, n of 250, level of 99% - Use mean formula

Percent of 25.8%, n of 500, level of 99% - Use percentage formula

b. Test the hypothesis and interpret your findings.

Hypothesis: mean=7.5, mean of 8.5, sd of 1.2, n of 670, level of 95%

The hypothesis is not supported.

Hypothesis: percent=86%, p of 95%, n of 1,000, level of 99%

The hypothesis is not supported.

Hypothesis: mean greater than 125, mean of 135, sd of 15, n of 500, level of 95%The hypothesis is supported.

Hypothesis: percent less than 33%, p of 31, n of 120, level of 99%

The hypothesis is not supported.

9. The manager of the aluminum recycling division of Environmental Services wants a survey which will tell him how many households in the city of Seattle, Washington, will voluntarily wash out, store, and then transport all of their aluminum cans to a central recycling center located in the downtown area and only open on Sunday mornings. A random survey of 500 households determines that 20% of households would do so and that each participating household expects to recycle about 100 cans monthly with a standard deviation of 30 cans. What is the value of parameter estimation in this instance?Application question. Parameter estimation will be useful in estimating the percent of households in the population who will take part in the recycling program, and it can be used to estimate the number of aluminum cans that each household will recycle monthly, on the average.

To estimate the percent of households, apply the confidence interval formula for a percent. The 95% level of confidence is used following.

To estimate the number of cans, apply the confidence interval formula for a mean. Note, however, that the sample size is only 100, although only 20% of the 500 respondents indicated they would recycle and gave an indication of the number of cans per month.

The 95% level of confidence is used below.

Combining the two estimates with the population of the city will yield an estimate of the total number of aluminum cans that would be recycled monthly. For instance, in a city of 100,000, the lower limit would be 100,000 times 13.7% times 94.1 cans per month, while the upper limit would be 100,000 times 26.3% times 105.9 cans per month.

10. It is reported in the newspaper that a survey sponsored by Forbes Magazine with Fortune 500 company executives has found that 75% believe that the United States trails Japan and Germany in automobile engineering. The article notes that executives were interviewed at a recent Bring the U.S. Back to Competitiveness symposium held on the campus of the University of Southern California. Why would it be incorrect for the article to report confidence intervals?

Application question. Students will need to identify the type of sample involved in the survey and determine if it embodies the assumptions of confidence intervals.

This is a convenience sample, and not a random probability sample. Confidence interval estimations assume random sampling.

11. Alamo Rent-A-Car executives believe that Alamo accounts for about 50% of all Cadilacs which are rented. To test this belief a researcher randomly identifies 20 major airports with on-site rental car lots. Observers are sent to each location and instructed to record the number of rental company Cadillacs observed in a four-hour period. About 500 are observed, and 30% are observed being returned to Alamo Rent-A-Car. What are the implications of this finding for the Alamo executives belief?Application question. Students will need to perform and interpret a hypothesis test for a percentage.

The executives have stated a hypothesis of p=50%. The sample information can be used to test the hypothesis as follows (using 95% level of confidence):

A computed z of -9.76 does not support the hypothesis.

CASE SOLUTIONSCase 16.1 Dont You Just Hate it When? (Part I)

Case ObjectiveThis is the first of a five part case with Marsha, an A student, and Josh, a student-athlete who does not pay attention to the concepts involved with statistical analyses. Students may relate to these series of cases as they sometimes have project team members who are not diligent.

In this case, students must realize that Josh has done descriptive statistics when he should have done inferential statistics. That is, he does means and percents instead of confidence intervals. They should also realize that Marsha can calculate these from the SPSS output.

Answers to Case Questions1. Dr. Zs requirement is for each team to present its statistical inference findings in class today. What analysis or analyses should have Josh done?For the means, Josh should have done One-Sample t-tests which provide the lower and upper bounds for 95% confidence intervals. For the percents, Josh should have calculated the confidence intervals using the percentage formula applied to the SPSS frequencies tables. 2. It is possible to make the presentation on the variables in the output file. Do what Marsha needs to do, now.

For the percentages, Marsha can calculate the 95% confidence intervals using the formula,

Here are the results.

pnSpLowerUpper

Use Pets, Pets, & Pets how often?44.4%1623.9%36.7%52.1%

Recommended PPP to a friend?82.1%1623.0%76.2%88.0%

Recall seeing a PPP newspaper ad in the past month?53.1%1623.9%45.4%60.8%

For the means, Marsha should use the confidence interval formula for a mean.

She can accomplish this by pasting Joshs table into Excel and using the formula to compute the lower and upper boundaries.

Times visited PPP in past yearAmount spent on last visit to PPPHow likely to buy at PPP next time (1-7 scale)Number of pets owned

NValid162162162162

Missing0000

Mean4.4$18.205.31.64

Mode41541

Std. Deviation4.980.851.50.77

Std. Error of Mean0.390.30.1180.061

Lower bound3.6$17.615.11.5

Upper bound5.2$18.795.51.8

Case 16.2 Auto Online Survey (Part II)

Case ObjectiveThis case study will require students to use SPSS with the Auto Online survey data set to compute confidence intervals and test hypotheses.

Answers to Case Questions

1. In order to describe this population, estimate the population parameters for the following.

a. How often they make purchases online.

The scale is 1= never to 5= very often, so it is an interval scale. The confidence interval for the mean should be determined using SPSS one-sample t test procedure. The output follows

The output reveals the mean to be 2.82, and the 95% confidence interval is 2.75 to 2.89.

b. Number of visits they made to Auto Online.

The number of visits is in the form of a ratio scale, so the one-sample, t test is used to determine the 95% confidence intervals. Here is the resulting SPSS output.

There is an average of 6.61 times, and the 95% confidence interval is 6.45 to 6.78 times.

c. The percentage who actually bought their vehicle from Auto Online.

SPSS does not have a capability of computing a confidence interval for a percentage. The solution is to have SPSS determine the sample percentage, and then to apply the percentage confidence interval equation to calculate the 95% confidence interval.

A total of 20.5% purchased their auto from Auto Online. Here is the calculation of the confidence interval.

d. The percentage of those who felt it was a better experience than buying at a traditional dealership.

This is also a percentage parameter estimation that requires SPSS Frequencies output to determine the mean and then an application of the percentage confidence interval formula.

Note that the sample size is 287, because the population relevant for those who felt it was a better experience includes only those who bought from Auto Online.

e. How do people feel about the Auto Online web site (question 6 on the questionnaire)?

There are six Likert-scale statements in question 6. Given that the scale is interval, one-sample t tests should be used to determine the 95% confidence intervals.

2. Auto Online principals have the following beliefs. Test these hypotheses.

a. People will strongly agree to all eight statements concerning use of the Internet and purchase (question 3 on the questionnaire).

This belief translates into hypotheses tests that the population mean for each statement in question 3 will be 3. The SPSS one-sample t test procedure should be used with the Test Value set to 3. The output follows.

The Sig (2-tailed) column reveals that all eight statements have significance levels of less than .01. In other words, there is no support (at the 95% level of confidence), that the average for any statement is 3.

b. Prior to buying a vehicle, people will visit the Auto Online web site approximately five times.

The hypothesis is that the number of visits to the Auto Online web site is equal to 5, and the SPSS one-sample t test procedure can test this hypothesis if the Test Value is set to 5. Here is the output.

The Significance level is .000, meaning that there is no support for the hypothesis. The true population mean is 6.61 (with confidence intervals).

c. Just about everyone will say that buying a vehicle online is a great deal better than buying it at a traditional dealership.

The scale is 1= a great deal better, and 4 = just a bit better. This is an interval scale, so the one-sample t test for a mean can be used with the Test Value set to 1.

The significance level of .000 indicates no support for the hypothesis. The experience of buying a vehicle online is not a great deal better than buying at a traditional auto dealership.

d. Those who buy their vehicles from Auto Online will be adults in their mid-thirties.

Note that only Auto Online buyers are mentioned in the claim. It is necessary to select only these respondents and to perform a one-sample t test using a Test Value of 35.

The hypothesis of 35 is not supported as the significance level is .000. However, the mean is actually 36.28, so buyers actually are in their mid-thirties.

e. Those who buy from Auto Online will pay an average of $3,500 below the sticker price, whereas those who buy elsewhere will pay only an average of $2,000 less than the vehicle sticker price.

It is necessary to compute a difference value with the SPSS Compute function (Diff=sticker-actual) that expresses the difference between the sticker price and that actual price paid for the automobile.

For the first value of $3,500, only Auto Online buyers are involved in analysis, so you must use data-select cases for didbuy=1. Then run the one-sample t test routine setting $3,500 as the test variable. Here is the output.

The mean is found to be $3,491 (rounded), and the significance level is .797. So there is no difference between the computed average and the hypothesized average, and the hypothesis is supported.

For the other group, select the data set to be only the respondents who did not use Auto Online, and run the test using $2,000 at the test value. The output follows.

The difference is found to be $2011 on the average, and the significance level is .478. So, at the .05 or 95% level of confidence, the hypothesis is supported.

It is apparent from this analysis, that Auto Online users pay a good deal less than the sticker price than do nonusers ($3500 versus $2000) for their vehicles.

Case 16.3 The Hobbits Choice Restaurant Survey Inferential Analysis

Case ObjectiveThis case study will require students to use SPSS with the Hobbits Choice integrated case dataset to compute confidence intervals and test hypotheses.

Answers to Case Questions

1. What are the population estimates for each of the following?

For a, b, and c, one must use SPSS to determine the percentage and then calculate the confidence interval for the percentage using the formula provided in the textbook. With d and e, the variables are ratio, so a one-sample t test should be used with the Test Value set to 0. For the age, one must calculate the age by subtracting the year born from present year (e.g., age=2006-yrborn).

a. Preference for easy listening radio programming

There were 385 respondents (15 do not listen to the radio), so the calculation of the confidence interval is as follows.

b. Viewing of 10 p.m. local news on TV

There were 356 respondents to the news show viewing question (44 do not watch the news), so the calculation of the confidence interval is as follows.

c. Subscribe to City Magazine

All 400 respondents are included in this confidence interval calculation.

d. Average age of heads of households

e. Average price paid for an evening meal entre

2. Because Jeff Deans restaurant will be upscale, it will appeal to high income consumers. Jeff hopes that at least 25% of the households have an income level of $100,000 or higher. Test this hypothesis.

The hypothesis can be tested by determining the 95% confidence interval for the percentage of the population that has an income of $100,000 or more.

This table indicates that a total of 27.3% (10.8% plus 16.5%) of the respondents reported an income of $100,000 or more. The confidence interval calculation is as follows.

The confidence level includes 25%, so the hypothesis is supported. If the confidence interval did not include 25% but was higher than 25%, the hypothesis would have strong support as Jeff hopes that at least 25% have high income.

3. With respect to those who are very likely to patronize the Hobbits Choice Restaurant, Jeff believes that they will either very strongly or somewhat prefer each of the following: (a) waitstaff with tuxedos, (b) unusual desserts, (c) large variety of entrees, (d) unusual entrees, (e) elegant dcor, and (f) jazz combo music. Does the survey support or refute Jeffs hypotheses? Interpret your findings.

This analysis first requires that only respondents who are very likely to patronize the Hobbits Choice Restaurant be selected from the larger sample.

Very strongly translates to a 5 on the Likert scale, so the first set of tests should be performed with a one-sample t test using a Test Value of 5.

There is no support for any of Jeffs very strongly prefers hypotheses. Lets try the strongly ones (Test Value=4).

Students may erroneously conclude that there is no support; however, this is true only for the jazz combo feature. All other means are greater than 4 and less than 5. That is, they are between very strongly and strongly prefer. Following are the 95% confidence intervals for the means to illustrate this finding.

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One-Sample Statistics

1400

2.82

1.304

.035

How often do you

make purchases

through the Internet?

N

Mean

Std. Deviation

Std. Error

Mean

One-Sample Statistics

1400

6.61

3.171

.085

About how many times

before you bought your

automobile did you visit

the Auto Online web site?

N

Mean

Std. Deviation

Std. Error

Mean

One-Sample Test

78.032

1399

.000

6.61

6.45

6.78

About how many times

before you bought your

automobile did you visit

the Auto Online web site?

t

df

Sig. (2-tailed)

Mean

Difference

Lower

Upper

95% Confidence

Interval of the

Difference

Test Value = 0

Did you buy your new vehicle on the Auto Online web site?

287

20.5

20.5

20.5

1113

79.5

79.5

100.0

1400

100.0

100.0

Yes

No

Total

Valid

Frequency

Percent

Valid Percent

Cumulative

Percent

One-Sample Statistics

1400

3.48

1.097

.029

1400

3.27

1.025

.027

1400

2.14

1.217

.033

1400

3.99

.657

.018

1400

4.36

.716

.019

1400

1.80

.404

.011

I found the web site was

very helpful in my

purchase.

I had a positive

experience using the

web site.

I would use this web

site only for research.

The web site influenced

me to buy my vehicle

I would feel secure to

buy from this web site.

Did you buy your new

vehicle on the Auto

Online web site?

N

Mean

Std. Deviation

Std. Error

Mean

One-Sample Test

118.793

1399

.000

3.48

3.43

3.54

119.467

1399

.000

3.27

3.22

3.33

65.818

1399

.000

2.14

2.08

2.20

226.797

1399

.000

3.99

3.95

4.02

227.676

1399

.000

4.36

4.32

4.39

166.308

1399

.000

1.80

1.77

1.82

I found the web site was

very helpful in my

purchase.

I had a positive

experience using the

web site.

I would use this web

site only for research.

The web site influenced

me to buy my vehicle

I would feel secure to

buy from this web site.

Did you buy your new

vehicle on the Auto

Online web site?

t

df

Sig. (2-tailed)

Mean

Difference

Lower

Upper

95% Confidence

Interval of the

Difference

Test Value = 0

One-Sample Statistics

1400

6.61

3.171

.085

About how many times

before you bought your

automobile did you visit

the Auto Online web site?

N

Mean

Std. Deviation

Std. Error

Mean

One-Sample Test

19.032

1399

.000

1.61

1.45

1.78

About how many times

before you bought your

automobile did you visit

the Auto Online web site?

t

df

Sig. (2-tailed)

Mean

Difference

Lower

Upper

95% Confidence

Interval of the

Difference

Test Value = 5

One-Sample Statistics

72

4.68

.470

.055

72

4.54

.502

.059

72

4.51

.503

.059

72

4.58

.496

.059

72

4.50

.504

.059

72

2.60

.944

.111

Prefer Formal Waitstaff

Wearing Tuxedos

Prefer Unusual Desserts

Prefer Large Variety of

Entrees

Prefer Unusual Entrees

Prefer Elegant Decor

Prefer Jazz Combo

N

Mean

Std. Deviation

Std. Error

Mean

One-Sample Test

12.299

71

.000

.68

.57

.79

9.160

71

.000

.54

.42

.66

8.664

71

.000

.51

.40

.63

9.970

71

.000

.58

.47

.70

8.426

71

.000

.50

.38

.62

-12.604

71

.000

-1.40

-1.62

-1.18

Prefer Formal Waitstaff

Wearing Tuxedos

Prefer Unusual Desserts

Prefer Large Variety of

Entrees

Prefer Unusual Entrees

Prefer Elegant Decor

Prefer Jazz Combo

t

df

Sig. (2-tailed)

Mean

Difference

Lower

Upper

95% Confidence

Interval of the

Difference

Test Value = 4

One-Sample Test

84.586

71

.000

4.68

4.57

4.79

76.805

71

.000

4.54

4.42

4.66

76.099

71

.000

4.51

4.40

4.63

78.335

71

.000

4.58

4.47

4.70

75.835

71

.000

4.50

4.38

4.62

23.337

71

.000

2.60

2.38

2.82

Prefer Formal Waitstaff

Wearing Tuxedos

Prefer Unusual Desserts

Prefer Large Variety of

Entrees

Prefer Unusual Entrees

Prefer Elegant Decor

Prefer Jazz Combo

t

df

Sig. (2-tailed)

Mean

Difference

Lower

Upper

95% Confidence

Interval of the

Difference

Test Value = 0

267PAGE 268

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