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CENGAGE MINDTAP Q Search Problem Set: Chapter 13 Two-Factor Analysis of Variance Back to Assignment y Tools Attempts Average / 3 13. A two-factor ANOVA: the null hypotheses, interpretation, and assumptions ips A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (jelly beans) for their 9:55 AM snack. Another group gets a high-protein snack (edamame) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the following questions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply. Does student performance on the test depend on the time of the test? Does the effect of the type of snack depend on the timing of the test? Do students who are tested at 11:00 AM score lower than students who are tested at 12:00 PM? Does the effect of the timing of the test depend on the type of snack the students eat? In the following table are the mean test scores for each of these nine different combinations of snack type and test timing. Factor B: Time of Test 10:00 AM 11:00 AM 12:00 PM Candy Snack M - 92.0 M - 84.0 M - 88.0 M = 88.0Factor B: Time of Test 10:00 AM 11:00 AM 12:00 PM Candy Snack M - 92.0 M = 84.0 M - 88.0 M = 88.0 Factor A: Type of Snack Protein Snack M - 88.5 M - 88.0 M - 87.5 M = 88.0 No Snack M = 90.0 M - 91.0 M = 83.0 M = 88.0 M - 90.2 M - 87.7 M - 86.2 The following graph shows the mean test scores for the treatment conditions. Use this graph and the data matrix to answer the following questions. 94 92 - 90 88 - candy snack 86 protein snack Mean Test Score no snack 84 82 78 10:00 AM 11:00 AM 12 00 PM Time Test Is AdministeredProblem Set: Chapter 13 Two-Factor Analysis of Variance 82 80 78 10:00 AM 11:00 AM 12:00 PM Time Test Is Administered Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of variance? Check all that apply. There is no interaction between the type of snack and the time of test H10:00 AM # H11:00 AM # 12:00 PM Hcandy = Mprotein = Uno snack Which of the following statements must the teacher assume in order to believe that the results of her two-factor ANOVA are valid? Check all that apply. The populations defined by the nine treatment conditions have equal means regardless of snack type or test time. The test scores within each of the nine samples (one for each treatment condition) are independent. The populations defined by the nine treatment conditions have equal variances regardless of snack type or test time. The populations defined by the nine treatment conditions are normally distributed. Grade It Now Save & Continue Continue without saving