Question

A random sample of students from each class was taken and student GPAs were recorded. Determine if there is evidence that the mean GPA is not the same for all three groups. Use a 0.10 level of significance.

Freshman	Sophomore	Junior
2.47	2.87	2.52
3.16	3.91	2.76
2.81	2.26	3.7
3.58	3.28	3.57
3.1	2.8	3.15
3.7	3.75	3.05
3.93	2.42	2.53
2.75	2.8	2.4

1.) What is the correct hypothesis statement?

2.) What is the value of the F-statistic for the one-way ANOVA? (Round to 4 decimal places)

3.) What is the p-value of the F statistic for the one-way ANOVA? (Round your answer to 4 decimal places.)

4.) Should the null hypothesis be rejected? (Use a 10% significance level) And should post-hoc tests be performed?

Answer 1

1) The following null and alternative hypotheses need to be tested:

Ho: μ1 = μ2 = μ3

Ha: Not all means are equal

2). To find the one-way ANOVA we have to find some of the summary measures of the data which are as follows

The one- way ANOVA is calculated using following formulas

F-statistic = MSB/MSW= 0.114/0.284= 0.401

3) p-value for f-statistic .6748 (from f-table at 90% confidence level)

4). Since the the p-vale for the F-statistic is 0.6748 > 0.10. So it is not significant at 90% confidence level. hence we fail to reject the null hypothesis and there is not enough evidence to claim that Not all means are equal.

Post-hoc test need not be performed since we fail to reject the null hypothesis.