Question

Now suppose that the p-value from the ANOVA F-test turns out to be 0.003. All of the following statements are false. Explain why each one is false.

a. The probability is 0.003 that the four groups have the same mean score.

b. The data provide very strong evidence that all four fonts produce different mean scores.

c. The data provide very strong evidence that the comic sans font produces a different mean score than the other fonts.

d. The data provide very little evidence that at least one of these fonts produces a different mean score than the others.

e. The data do not allow for drawing a cause-and-effect conclusion between font and exam score.

f. Conclusions from this analysis can be generalized to the population of all students at the instructor’s school.

Answer 1

a. This statement is false because p-value gives actual probability of rejecting null hypothesis when it is true.

b. This statement is false because we state alternative hypothesis that at least one mean score is significantly different than other. We can not say any thing about all means.

c. This statement is false because from available result we can't say which mean score is different from mean score of remaining groups. For this we need to perform multiple comparison test.

d. Since p-value is very small, the data provide very strong evidence that at least one of these fonts produces a different mean score than the others.

f. Please provide complete question background.