Question

4. Claire, Tian and Chris, another three committee members who are interested in students' academic success, would like to check if there is a difference between the average GPA of Varsity&Club athletes 'VarsClub') and the average GPA of Intramural&Non-athletes 'IntramNon). A. Indicate what inference procedure you would use to investigate this question. Why? B. Write appropriate hypotheses. C. Assume the assumptions for the test are met. Partial Remdr output is given below. Use the output to complete the test procedure at a .10 significance level data: GPA2 by Sport2 1.0405, df= 151.606, p-value=-- alternative hypothesis: true difference in means ('IntramNon'-VarsClub') is not equal to 0 sample estimates: mean in group IntramNon mean in group VarsClub 3.530119 3.579211 P-value: Conclusion: Given your conclusion above, which type of error (Type I or Type lI) could be made? Explain this type of error in context D.

Answer 1

(A) 2 independent sample t test

because population SD not provided.

(B)

H0: Nul Hypothesis: $\mu 1=\mu 2$

HA: Alternative Hypothesis: $\mu 1\neq \mu 2$

(C)

(i)

t score = 1.0405

ndf = 151.606

Two Tail Test

By Technology, P - Value = 0.2998

So,

P - Value = 0.2998

(ii)

Since P - Value = 0.2998 is greater than $\alpha$ = 0.10, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that there is difference between average GPA of Varsity & Club athletes and the average GPA of Intramural & Non- athletes.

(D)

Since the conclusion is : Fail to reject null hypothesis, Type II Error: Failure to reject a false null hypothesis could be made.

Explanation:
Suppose in reality there is difference between average GPA of Varsity & Club athletes and the average GPA of Intramural & Non- athletes.But, we wrongly conclude that there is no significant difference between average GPA of Varsity & Club athletes and the average GPA of Intramural & Non- athletes. Type II Error is committed in this situation.