In order to better prepare for her 8:00am classes, a statistics student designs an experiment to see how various strategies improve test scores. Completing homework assignments and eating a good breakfast are often said to be good ways to improve focus for class. She assigns half of her students homework assignments to practice and half no additional homework assignments. Within these groups, half of the participants are instructed to eat a balanced breakfast the morning of the test and the other half are asked to skip breakfast. She then measures exam performance on a test with scores ranging from 1-10.(50 points)

No Homework

Homework

Eating Breakfast

7

3

6

7

8

4

6

8

10

10

9

8

8

10

Skipping Breakfast

6

7

9

6

9

7

8

7

6

7

9

8

6

8

a)What kind of test would you need to run?

The type of test that we would need to run is a Two-way ANOVA with replication

b)What is the independent variable (or factor)?

The independent variable from this data is various strategies

c)What is the dependent variable?

The dependent variable are the test scores

d)What is the statistical notation (for some types of tests, this answer should include the post-hoc notations AS WELL as the overall statistical notation)?

e)Is the test significant? How do you know? (for some types of tests, this answer should include the post-hoc significance AS WELL as the overall significance)

From the table of test of between subject effect we can see than p values of the main effect breakfast is 0.888, which is greater than 0.05, hence the effect of breakfast is not significant.

We can see that the p value of the effect homework is 0.006, which is less than the significance level of 0.05, hence the effect of homework is significant

The p value of the interaction term breakfast and homework is 0.003, which is less than 0.05, hence we can say that there is significant effect of interaction in deciding the test scores

f)What are the means that should be reported (If this is an ANOVA/factorial please include all means to be reported)?

g)What is the complete interpretation (in order to receive full credit you need to include all statistical notation as well as an interpretation of what they mean in context)