Question

Is there any systematic tendency for part-time college faculty to hold their students to different standards than do full-time faculty? An article reported that for a sample of 125 courses taught by full-time faculty, the mean course GPA was 2.7386 and the standard deviation was 0.66342, whereas for a sample of 88 courses taught by part-timers, the mean and standard deviation were 2.8439 and 0.52241, respectively. Does it appear that true average course GPA for part-time faculty differs from that for faculty teaching full-time? Test the appropriate hypotheses at significance level 0.01.

State the relevant hypotheses.

H₀: μ_full-time − μ_part-time = 0
H_a: μ_full-time − μ_part-time < 0H₀: μ_full-time − μ_part-time = 0
H_a: μ_full-time − μ_part-time ≤ 0    H₀: μ_full-time − μ_part-time = 0
H_a: μ_full-time − μ_part-time ≠ 0H₀: μ_full-time − μ_part-time = 0
H_a: μ_full-time − μ_part-time ≥ 0H₀: μ_full-time − μ_part-time = 0
H_a: μ_full-time − μ_part-time > 0

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=P-value=

State the conclusion in the problem context.

Reject H₀. The data suggests that the true average course GPA for part-time faculty differs from that for faculty teaching full-time.Fail to reject H₀. The data suggests that the true average course GPA for part-time faculty differs from that for faculty teaching full-time.    Fail to reject H₀. The data does not suggest that the true average course GPA for part-time faculty differs from that for faculty teaching full-time.Reject H₀. The data does not suggest that the true average course GPA for part-time faculty differs from that for faculty teaching full-time.

Answer 1

H₀: μ_full-time − μ_part-time = 0

H_a: μ_full-time − μ_part-time ≠ 0

Test Statistic :-


t = -1.29

Test Criteria :-
Reject null hypothesis if


DF = 208


Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.294 ) = 0.1971
Reject null hypothesis if P value < level of significance
P - value = 0.1971 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

Fail to reject H₀. The data does not suggest that the true average course GPA for part-time faculty differs from that for faculty teaching full-time.