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 (cheese) 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). 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 μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM = μ12:00 PM12:00 PM 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 populations defined by the nine treatment conditions have different variances depending on type of snack and test time. The populations defined by the nine treatment conditions are normally distributed. The populations defined by the nine treatment conditions have equal variances regardless of snack type or test time. Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the followingquestions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply.Does the effect of the timing of the test depend on the type of snack the students eat?Is there a difference among the scores for the test times because fourth graders are more alert in the morning?Does the effect of the type of snack depend on the timing of the test?Do students who eat a candy snack score higher than students who have a protein snack?In the following table are the mean test scores for each of these nine different combinations of snack type and test timing.Factor A: Type of SnackMean Test Score9492-9088The following graph shows the mean test scores for the treatment conditions. Use this graph and the data matrix to answer the following questions.86T84828078Factor B: Time of Test10:00 AMM = 92.0M = 88.5M = 90.0M = 90.210:00 AMCandy SnackProtein SnackNo Snack11:00 AMTime Test Is Administered11:00 AMM = 84.0M = 88.0M = 91.0M = 87.712:00 PM12:00 PMM = 88.0M = 87.5M = 83.0M = 86.2-candy snackprotein snackno snackM = 88.0M = 88.0M = 88.0Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis ofvariance? Check all that apply.0

Question

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 (cheese) 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).   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 μ10:00 AM10:00 AM ≠ μ11:00 AM11:00 AM ≠ μ12:00 PM12:00 PM μ10:00 AM10:00 AM = μ11:00 AM11:00 AM = μ12:00 PM12:00 PM  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 populations defined by the nine treatment conditions have different variances depending on type of snack and test time. The populations defined by the nine treatment conditions are normally distributed. The populations defined by the nine treatment conditions have equal variances regardless of snack type or test time. Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the followingquestions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply.Does the effect of the timing of the test depend on the type of snack the students eat?Is there a difference among the scores for the test times because fourth graders are more alert in the morning?Does the effect of the type of snack depend on the timing of the test?Do students who eat a candy snack score higher than students who have a protein snack?In the following table are the mean test scores for each of these nine different combinations of snack type and test timing.Factor A: Type of SnackMean Test Score9492-9088The following graph shows the mean test scores for the treatment conditions. Use this graph and the data matrix to answer the following questions.86T84828078Factor B: Time of Test10:00 AMM = 92.0M = 88.5M = 90.0M = 90.210:00 AMCandy SnackProtein SnackNo Snack11:00 AMTime Test Is Administered11:00 AMM = 84.0M = 88.0M = 91.0M = 87.712:00 PM12:00 PMM = 88.0M = 87.5M = 83.0M = 86.2-candy snackprotein snackno snackM = 88.0M = 88.0M = 88.0Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis ofvariance? Check all that apply.0

Accepted Answer

Analysis of variance