SECTION 12.2 EXERCISES

For Exercises 12.27 and 12.28, see page 677 for Exercises 12.29 and 12.30, see page 681 and for Exercises 12.31 and 12.32, see page 685.

Question 12.33

12.33 College dining facilities. University and college food service operations have been trying to keep up with the growing expectations of consumers with regard to the overall campus dining experience. Because customer satisfaction has been shown to be associated with repeat patronage and new customers through word-of-mouth, a public university in the Midwest took a sample of patrons from their eating establishments and asked them about their overall dining satisfaction.9 The following table summarizes the results for three groups of patrons:

Category n s
Student—meal plan 3.44 489 0.804
Faculty—meal plan 4.04 69 0.824
Student—no meal plan 3.47 212 0.657

  1. (a) Is it reasonable to use a pooled standard deviation for these data? Why or why not? If yes, compute it.

  2. (b) The ANOVA F statistic was reported as 17.66. Give the degrees of freedom and either an approximate (from a table) or an exact (from software) P-value. Sketch a picture of the F distribution that illustrates the P-value. What do you conclude?

  3. (c) Prior to performing this survey, food service operations thought that satisfaction among faculty would be higher than satisfaction among students. Use the results in the table to test this contrast. Make sure to specify the null and alternative hypotheses, test statistic, and P-value.

686

Question 12.34

12.34 Writing contrasts. You’ve been asked to help some administrators analyze survey data on textbook expenditures collected at a large public university. Let μ1, μ2, μ3, and μ4 represent the population mean expenditures on textbooks for the freshmen, sophomores, juniors, and seniors, respectively.

  1. (a) Because freshman and sophomores take lower-level courses, which might use more expensive introductory textbooks, the administrators want to compare the average of the freshmen and sophomores with the average of the juniors and seniors. Write a contrast that expresses this comparison.

  2. (b) Write a contrast for comparing the freshmen with the sophomores.

  3. (c) Write a contrast for comparing the juniors with the seniors.

Question 12.35

12.35 Writing contrasts, continued. Return to the eye study described in Example 12.15 (page 663). Let μ1, μ2, μ3, and μ4 represent the mean scores for blue, brown, gaze down, and green eyes, respectively.

  1. (a) Because a majority of the population in this study are Hispanic (eye color predominantly brown), we want to compare the average score of the brown eyes with the average of the other two eye colors. Write a contrast that expresses this comparison.

  2. (b) Write a contrast to compare the average score when the model is looking at you versus the score when looking down.

Question 12.36

12.36 Analyzing contrasts. Answer the following questions for the two contrasts that you defined in the previous exercise.

  1. (a) For each contrast, give H0 and an appropriate Ha. In choosing the alternatives, you should use information given in the description of the problem, but you may not consider any impressions obtained by inspection of the sample means.

  2. (b) Find the values of the corresponding sample contrasts c1 and c2.

  3. (c) Calculate the standard errors and .

  4. (d) Give the test statistics and approximate P-values for the two significance tests. What do you conclude?

  5. (e) Compute 95% confidence intervals for the two contrasts.

Question 12.37

12.37 Two contrasts of interest for the stimulant study. Refer to Exercise 12.23 (page 669). There are two comparisons of interest to the experimenter. They are (1) placebo versus the average of the two low-dose treatments and (2) the difference between High A and Low A versus the difference between High B and Low B.

  1. (a) Express each contrast in terms of the means (μ’s) of the treatments.

  2. (b) Give estimates with standard errors for each of the contrasts.

  3. (c) Perform the significance tests for the contrasts. Summarize the results of your tests and your conclusions.

Question 12.38

12.38 Multitasking with technology in the classroom. Laptops and other digital technologies with wireless access to the Internet are becoming more and more common in the classroom. While numerous studies have shown that these technologies can be used effectively as part of teaching, there is concern that these technologies can also distract learners if used for off-task behaviors.

In one study that looked at the effects of off-task multitasking with digital technologies in the classroom, a total of 145 undergraduates were randomly assigned to one of seven conditions.10 Each condition involved a task that was conducted simultaneously with a class lecture. The study consisted of three 20-minute lectures, each followed by a 15-item quiz. The following table summarizes the conditions and quiz results (mean proportion correct).

Condition n Lecture 1 Lecture 2 Lecture 3
Texting 21 0.57 0.75 0.56
Email 20 0.52 0.69 0.50
Facebook 20 0.50 0.68 0.43
MSN messaging 21 0.48 0.71 0.42
Natural use control 21 0.50 0.78 0.58
Word-processing control 21 0.55 0.75 0.57
Paper-and-pencil control 21 0.60 0.74 0.53

  1. (a) For this analysis, let’s consider the average of the three quizzes as the response. Compute this mean for each condition.

  2. (b) The analysis of these average scores results in and . Test the null hypothesis that the mean scores across all conditions are equal.

  3. (c) Using the marginal means from part (a) and the Bonferroni multiple-comparisons method, determine which pairs of means differ significantly at the 0.05 significance level. (Hint: There are 21 pairwise comparisons, so the critical t-value is 3.095. Also, it is best to order the means from smallest to largest to help with pairwise comparisons)

  4. (d) Summarize your results from parts (b) and (c) in a short report.

687

Question 12.39

12.39 Contrasts for multitasking. Refer to the previous exercise. Let μ1, μ2, . . . , μ7 represent the mean scores for the seven conditions. The first four conditions refer to off-task behaviors, while the last three conditions represent different sorts of controls.

  1. (a) The researchers hypothesized that the average score for the off-task behaviors would be lower than that for the paper-and-pencil control condition. Write a contrast that expresses this comparison.

  2. (b) For this contrast, give H0 and an appropriate Ha.

  3. (c) Calculate the test statistic and approximate P-value for the significance test. What do you conclude?

Question 12.40

12.40 Power calculations for planning a study. You are planning a new eye gaze study for a different university than that studied in Example 12.15 (page 663). From Example 12.15, we know that the standard deviations for the four groups considered in that study were 1.75, 1.72, 1.53, and 1.67. In Figure 12.9, we found the pooled standard error to be 1.68. Because the power of the F test decreases as the standard deviation increases, use σ = 2.0 for the calculations in this exercise. This choice leads to sample sizes that are perhaps a little larger than we need but prevents us from choosing sample sizes that are too small to detect the effects of interest. You would like to conclude that the population means are different when μ1 = 3.2, μ2 = 3.7, μ3 = 3.0 and μ4 = 4.0.

  1. (a) Pick several values for n (the number of students that you will select from each group) and calculate the power of the ANOVA F test for each of your choices.

  2. (b) Plot the power versus the sample size. Describe the general shape of the plot.

  3. (c) What choice of n would you choose for your study? Give reasons for your answer.

Question 12.41

12.41 Power for a different alternative. Refer to the previous exercise. Suppose we increase μ4 to 4.2. For each of the choices of n in the previous example, would the power be larger or smaller under this new set of alternative means? Explain your answer.