Studies in the New York City schools investigated different reading programs to see how well children learned to read with each program. The first reading program focused heavily on nonfiction texts, the second focused more on fiction texts, while the third was evenly split between fiction and nonfiction. In all, 43 students participated in the study. Reading ability was measured using a test on which students could score between 0 and 100 points. To investigate any differences in the population average reading scores across the three groups, the principal investigator conducted an ANOVA test.
a. Provide the hypotheses the researcher wishes to test.

b. The ANOVA test resulted in a test statistic of F=3.85 with a corresponding p-value of 0.032. If there really was no difference in the population mean reading scores for the three reading programs, what is the distribution of the test statistic?

i. F(2,40) distribution
ii. F(3,43) distribution
iii. t(42) distribution
iv. N(0,1) distribution

c. Select the corresponding decision at a 5% level.

i. Reject the null hypothesis.
ii. Fail to reject the null hypothesis.

d. In one simple sentence, provide the appropriate conclusion the principal investigator should include in her report.