Question

Please answer all of the following question correctly, showing all steps and reasoning necessary.

Part 3 One sample test (50 points) A researcher is interested in determining whether or not review sessions affect exam performance. Based on information gathered in previous semesters, the researcher knows that the population of students who do not receive review sessions follows a normal distribution with a mean of 25 and a standard deviation of 5. A review session is administered to a sample of students (n-9) in an attempt to determine if this has an effect on the exam performance. The average exam performance of this sample is 28 A. Is there evidence that students receiving a review session perform differently compared to those who do not? Show all the steps in hypothesis testing. (20 points)

Answer 1

(A)

Data:     

n = 9   

μ = 25   

s = 5   

x-bar = 28   

Hypotheses:

Ho: μ = 25   

Ha: μ ≠ 25   

Decision Rule:

α = 0.05   

Lower Critical z- score = -1.959963985

Upper Critical z- score = 1.959963985

Reject Ho if |z| > 1.959963985

Test Statistic:

SE = s/sqrt n = 5/√9 = 1.666666667

z = (x-bar - μ)/SE = (28 - 25)/1.66666666666667 = 1.8

p- value = 0.071860638   

Decision (in terms of the hypotheses):

Since 1.8 < 1.959963985 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that students receiving review sessions perform differently

(B)

Data:     

n = 9   

μ = 25   

s = 5   

x-bar = 28   

Hypotheses:   

Ho: μ ≤ 25   

Ha: μ > 25   

Decision Rule:   

α = 0.05   

Critical z- score = 1.644853627   

Reject Ho if z > 1.644853627   

Test Statistic:   

SE = s/sqrt n = 5/√9 = 1.666666667

z = (x-bar - μ)/SE = (28 - 25)/1.66666666666667 = 1.8

p- value = 0.035930319   

Decision (in terms of the hypotheses):   

Since 1.8 < 1.644853627 we fail to reject Ho

Conclusion (in terms of the problem):   

There is no sufficient evidence that students receiving review sessions perform better.