Question

8) A professor has decided that students should be allowed to do only the work they wish to do in undergraduate statistics. So she uploaded 15 weekly assignments. Students see their scores when they complete the assignments. But the homework assignments are not required – they are discretionary. Students take the final exam and the exam grade is the final grade. The results for this class of 80 students gave an average exam score of 72. These sample results of 80 students are used to test the claim that the overall population mean grade is higher than 70. Population standard deviation σ is 7.3.

a)  What is the value of the sample average exam score?

b)  What is the value of the population average exam score?

c) What is the sample size?

d) State the null hypothesis

e) State the alternative hypothesis

f) What is the value of the test statistic (z test)?

g) What is the p-value?

h) What is your conclusion regarding the claim about the mean grade at 5% level?

Answer 1

a) sample average exam score xbar = 72

b) population average exam score = 70

c) sample size n = 80

d) null hypothesis Ho : = 70

e) alternative hypothesis H1 : > 70

f) test statistic Z = ( xbar - )/(/√n)

Z = (72-70)/(7.3/√80)

Z = 2.45

g) p-value for Z = 2.45 and right tailed test

p-value = P( Z > 2.45)

p-value = 0.0071

h) Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our p-value = 0.0071 < 0.05

We fail to reject Ho

Conclusion : There is sufficient evidence to support the claim that the overall population mean grade is higher than 70.