A sociology student wanted to test to see if the GPA’s of four sororities were s

Question

A sociology student wanted to test to see if the GPA’s of four sororities were signi?cantly di?erent. They found the following: Let A = group 1, B = group 2, C = group 3, and D = group 4. Assume ? = 0.05.

(a) State the null and alternative hypothesis mathematically.

(b) State the null and alternative hypothesis in terms ofthe problem.

(c) Calculate the range for the p-value.

(d) Interpret the p-value in terms of the problem.

(e) Do you reject or fail to reject the null hypothesis?

(f) Interpret your conclusion in terms of the problem.

(g) What 95% con?dence interval between two means will certainly not contain zero if we were to create it?

(h) What type of error could we have made in this question?

(i) Interpret a Type II error in terms of the problem.

Explanation / Answer

(a) Null hypothesis: µ1= µ2= µ3= µ4, Alternative Hypothesis: Two or more means are different from the rest

(b) Null hypothesis: The gpas of the four sororities are not significantly different. Alternative hypothesis: There is a significant difference in the gpas of the four sororities.

(c) I wasn't very clear on what was meant by range of the p value. By Anova calculations, the p value is 0.0005. However, if additionally, we perform the Tukey Honestly Significant Difference( which is a program that can be found online) then we will get the following table

Group 1 vs Group 2: Diff=0.3500, 95%CI=-0.0805 to 0.7805, p=0.1456
Group 1 vs Group 3: Diff=-0.3500, 95%CI=-0.7805 to 0.0805, p=0.1456
Group 1 vs Group 4: Diff=-0.2400, 95%CI=-0.6705 to 0.1905, p=0.4473
Group 2 vs Group 3: Diff=-0.7000, 95%CI=-1.1305 to -0.2695, p=0.0005
Group 2 vs Group 4: Diff=-0.5900, 95%CI=-1.0205 to -0.1595, p=0.0039
Group 3 vs Group 4: Diff=0.1100, 95%CI=-0.3205 to 0.5405, p=0.9010

In which case, the range of the p values will be from 0.0005 to 0.9010

This table is used to show which groups are significantly different from the rest.

(d) . A smaller p value usually indicates strong evidence against the null hypothesis leading to its rejection. Here the value of p=0.005 which is less than the significance level so we lean toward rejecting the null hypothesis. In this problem, the p value shows that there is a stronger possibility of the alternative hypothesis( two or more means being different from the rest).

(e) We reject the null hypothesis because p is a very low number<0.05.

(f) By rejecting the null hypothesis, we reject the statement that there is no difference between the mean gpas of the four sororities

(h) In this problem, we could have made a Type II error, i.e accepting the null hypothesis when it was actually false.

(i) A type II error here would have meant that we would have reached the conclusion that the null hypothesis which states that there is no difference in the gpas of the four sororities is true, even though it is not.

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