Question

You will perform an ANOVA test. For the hypothesis test make sure to report the following steps:

1. Identify the null hypothesis, Ho, and the alternative hypothesis, Ha.
2. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
3. Find the critical value(s) and identify the rejection region(s).
4. Find the appropriate standardized test statistic. If convenient, use technology.
5. Decide whether to reject or fail to reject the null hypothesis.
6. Interpret the decision in the context of the original claim.

The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Test the claim that at least one group has a different mean. Use α = 0.05.

Tennis	Golf	Swimming
2.6 3.2 2.5 3.5 3.1 2.1	1.8 3.3 1.9 2.1	2.7 2.5 2.8 3.0 2.5

Answer 1

We can perform ANOVA using excel .

Go to Data menu ---> data analysis ----> Select Anova: Single Factor

For Input range select the entire data table ( with headings ).

Check the box for "Labels in the first Row" . ( If you did not selected the column headings then do not need to check this box )

Then click on OK.

The analysis output will be as follows :

H₀ : The grade point averages of students participating in each sports is same

H_a : The grade point average of students for at least one sport type is different.

This is two tail test

Critical value :

From ANOVA table F_crit = 3.885

Rejection region :

Reject H0, if F ≥ F_crit , otherwise fail to reject H₀  

test statistic :

From table F = 1.56

Decision rule : As F is less than F_crit , We fail to reject H₀   

Conclusion : There is no significant evidence that the grade point average of students for at least one sport type is different, that is averages are same for all sports.