A researcher wants to know if the clothes a woman wears is a factor in her GPA.

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.

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 0.05.

Ha: At least two of the means are different from each other.

Calculate the p-Value.

p-Value =                            [ Select ]                       ["0.2529", "0.0480", "0.3471", "0.0256"]      

                           [ Select ]                       ["There is insufficient evidence to support the claim that at least two of the mean GPAs differ from each other.", "There is sufficient evidence to support the claim that at least two of the mean GPAs differ from each other."]      

Dress Jeans Skirt Shorts 3.2 3.9 3.3 4.0 2.7 2.6 2.0 3.4 3.6 3.7 2.5 3.6 3.0 3.5 3.4 3.7 3.1 1.5

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

p - Value = 0.0480

There is sufficient evidence to support the claim that at least two of the mean GPAs differ from each other.

Column n Mean Std. Dev. Std. Error Dress 4 3.125 0.37749172 0.18874586 Jeans 5 3.36 0.51768716 0.23151674 Skirt 5 2.54 0.82036577 0.36687873 Shorts 4 3.675 0.25 0.125

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