Question

The university is interested in investigating whether the mean GPA of all college students differs for various years in college. Samples were selected and the data was analyzed in Statistix to determine if the average GPA of sophomores, juniors, and seniors differed. The analysis is shown below:

One-Way AOV for GPA by Year

Source DF SS MS F P
Year 2 2.7978 1.39889 9.81 0.0001
Error 85 12.1163 0.14255
Total 87 14.9141

Grand Mean 3.2259 CV 11.70

Bonferroni All-Pairwise Comparisons Test of GPA by Year

Year Mean Homogeneous Groups
Sophomore 3.7500 A
Junior 3.1847 B
Senior 3.1360 B

Alpha 0.05

Which conclusion is correct when conducting the test of hypothesis at alpha=.01?

There is sufficient evidence to indicate that at least two of the population mean GPAs differ for the three years of students.

There is sufficient evidence to indicate that all three population mean GPAs differ for the three years of students.

There is insufficient evidence to indicate that at least two of the population mean GPAs differ for the three years of students.

The mean GPA of all sophomores exceeds the mean GPA of the other two groups.

Answer 1

The p-value is 0.0001 which is less than the alpha=.01, so , we reject the null hypothesis and conclude that there is sufficient evidence to indicate that at least two of the population mean GPAs differ for the three years of students.

Bonferroni All-Pairwise Comparisons Test is performed at Alpha 0.05 and it shows that the mean GPA of Sophomore is significantly different from other two groups/ So, at alpha=.05, The mean GPA of all sophomores exceeds the mean GPA of the other two groups. But that may not be correct for alpha=.01

So, the correct option is,

There is sufficient evidence to indicate that at least two of the population mean GPAs differ for the three years of students.