Question

EKU knows that on average 8.7 percent of students with a standard deviation of 3.0 will fail an EKU course. The psychology department wanted to know if their summer courses had a similar number of failing students. Dr. Lawson looked at the failing rates for the most recent summer courses (9 courses) and got the following data Use a single-sample z-test to determine the outcome (alpha- 05, two-tailed). Class 1: 11.0 % failed Class 2: 8.4 % failed Class 3: 10.2 % failed Class 4: 9.4 % failed Class 5: 6.8 % failed Class 6: 13.0 % failed Class 7: 6.8 % failed Class 8: 9.8 % failed Class 9:11.9 % failed In the box below, provide the following information: Null Hypothesis in sentence form (1 point): Alternative Hypothesis in sentence form (1 point): Critical Value(s) (2 points) Calculations (4 points): Note: the more detail you provide, the more partial credit that I can give you if you make a mistake. Outcome (determination of significance or not, and what this reflects in everyday language, 2 points)

Answer 1

Data:    

n = 9   

μ = 8.7   

s = 3   

x-bar = 9.7   

Hypotheses:   

Ho: μ = 8.7 (The mean failing rate is 8.7%)

Ha: μ ≠ 8.7 (The mean failing rate is different from 8.7%)

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/√n = 3/√9 = 1

z = (x-bar - μ)/SE = (9.7 - 8.7)/1 = 1

p- value = 0.317310508   

Decision (in terms of the hypotheses):

Since 1 < 1.959963985 we fail to reject Ho

Conclusion (in terms of the problem):

There is no sufficient evidence that the mean failing rate is different from 8.7%