Hi! Can someone please help me answer these questions? Please keep in mind that

Question

Hi! Can someone please help me answer these questions? Please keep in mind that more than one answer is possible for each of the multiple choice questions.
Thank you very much!!!

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 (gummy bears) for their 9:55 AM snack. Another group gets a high-protein snack (tofu) 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? Check all that apply. (Note: Assume that receiving no snack is considered one type of snack.) Is there a difference among the scores for the snack types because a candy snack makes it harder for students to focus on the test? Do students who are tested at 12:00 PM score higher than students who are tested at 11:00 AM? Do students who eat a candy snack score higher than students who have no snack? Does the effect of the type of snack depend on the timing of the test? In the following table are the mean test scores for each of these nine different combinations of snack type and test timing

Explanation / Answer

Part (a)

ANOVA can only say if there is a difference in the effect among the treatment groups. But, it cannot throw any light on whether a particular treatment effect is more than one other treatment effect. The latter can be assessed only by a post hoc test. With particular reference to the given question, ANOVA can only say if different snacks have different effects or different test timing have different effect and also say if different snack-timing combinations have different effects (this is termed as ‘interaction’ effect). But, it cannot say if candy is better than protein snack with respect to test score or 12 noon is a better timing than 10 am with respect to test score. It can of course say if snack-timing combinations have varying effects as a whole, but not individually.

Based on this, answer to the question is: first and the last questions can be answered by ANOVA.      

ANSWER

Part (b)

With respect to the timings, the graph shows a downward trend from 10 to 11 to 12. The mean figure comes down from 90.2 to 87.7 to 86.2. Thus, it would be right to guess that the means are different and hence first hypothesis is likely to be accepted, which, in turn implies third will be rejected.

If there is no interaction between snack and timing, in an ideal situation, the graph for a particular snack over the timing would be a straight line. This is more or less true for ‘red’ graph (protein snack), but not so for others. Also, taking two extremes, candy-10 is 92 while no-snack-12 is just 83. These two should lead us to believe the interaction effect is significant, implying second hypothesis will be rejected.

Thus, second and third hypotheses are likely to be rejected. ANSWER

Part (c)

The ANOVA model is

xijk = µ + i + j + ij + ijk, where xijk represent the kth observation in the kth cell of ith row-jth column, µ = common effect, i = effect of ith row, j = effect of jth column, ij = row-column interaction and ijk is the error component which is assumed to be iid Normally Distributed with mean 0 and variance 2.

Assumption on ijk => xijk are independent and normally distributed.

Thus, only statement 1 and 3 are valid. ANSWER

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.