Question

Survey 40 people and ask them this question: “How many days a week do you typically exercise?” You calculated your average for the results, and standard deviation and standard error. The following are your results:

Average: 4.8625

Standard Deviation: 1.1602

Standard Error: 0.1834

You then ask a friend what they think the average value is for a person who typically exercises during the week. Your friend claims the average to be 4.

1. What are the appropriate null and alternative hypotheses to test the claim made by your friend?

2. What is the value of the test statistic? SHOW ALL CALCULATIONS.

3. What is the p-value for the test? SHOW HOW YOU GOT THIS VALUE.

4. What is your conclusion regarding the “claim” this person made about the average value? GIVE THE FULL CONCLUSION, INCLUDING A “REJECT” or “DO NOT REJECT” STATEMENT AND THE MEANING OF THE CONCLUSION.

Answer 1

1) Null and alternative hypotheses

Ho : = 4

H1 : 4

2) test statistic t

t = ( xbar - )/(s/√n)

t = ( 4.8625 - 4)/(1.1602/√40)

t = 4.70

3) p-value for t = 4.70 and d.f = n -1 = 39 , two tailed test

p-value = 2 * P( t >4.70) d.f = 39

p-value = 0.00003

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

Our p-value = 0.00003 < 0.05

Decision : Reject Ho

Conclusion : There is no sufficient evidence to support the claim the average days exerciseexercise in a week is 4