Question

A researcher wants to know if the clothes a woman wears is a factor in her GPA. The table below shows data that was collected from a survey.

Shorts	Dress	Jeans	Skirt
3.9	2.6	2.7	3.4
2.1	2.6	1.8	3.5
2.4	2.3	3	3.5
2	2.1	4	3.8
3.7	2.6	2.3	3.2
2.5	2.6	2.8	3.5
3.6	1.9	2.9	2.9
2.2	2.3	2.2	2.1
2.7			3.5

Assume that all distributions are normal, the four population standard deviations are all the same, and the data was collected independently and randomly. Use a level of significance of α=0.1α=0.1.





H0: μ1=μ2=μ3=μ4

H1: At least two of the means differ from each other.

1. For this study, we should use Select an answer:
2. The test-statistic for this data =_____ (Please show your answer to 3 decimal places.)
3. The p-value for this sample =_______ (Please show your answer to 4 decimal places

Answer 1

Excel output:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Shorts	9	25.1	2.788889	0.551111
Dress	8	19	2.375	0.073571
Jeans	8	21.7	2.7125	0.435536
Skirt	9	29.4	3.266667	0.2525
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3.467361111	3	1.155787	3.469915	0.028253	2.922277
Within Groups	9.992638889	30	0.333088
Total	13.46	33

1. The test-statistic for this data =3.470
2. The p-value for this sample =0.0283