Question

A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You want to test this claim. You find that a random sample of 33 cardholders has a mean credit card balance of $5,232 and a standard deviation of $675. At alpha α= 0.01​ can you support the​ claim? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.​

(a) Write the claim mathematically and identify H0 and Ha.

Which of the following correctly states H0 and Ha​?

A.

H0​: μ > ​$5,000

Ha​: μ ≤ ​$5,000

B.

H0​: μ > ​$5,000

Ha​: μ ≤ ​$5,000

C.

H0​: μ =​ $5,000

Ha​: μ ≠ ​$5,000

D.

H0​: μ ≤ ​$5,000

Ha​: μ > ​$5 comma 0005,000

E.

H0​: μ = ​$5,000

Ha​: μ > ​$5,000

F.

H0​: μ ≥ ​$5,000

Ha​: μ < ​$5,000

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

What​ is(are) the critical​ value(s) t0​?

t0= ____? ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed

Determine the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice.

​(Round to three decimal places as​ needed.)

A. t < ____

B. _____ < t < _____

C. t < _____ and t > _____

D. t > _____

​(c) Find the standardized test statistic t.

t = ______ ​(Round to two decimal places as​ needed.)

​

(d) Decide whether to reject or fail to reject the null hypothesis.

A. Reject H0because the test statistic is not in the rejection region.

B. Fail to reject H0 because the test statistic is not in the rejection region.

C. Reject H0 because the test statistic is in the rejection region.

D. Fail to reject H0because the test statistic is in the rejection region.

​(e) Interpret the decision in the context of the original claim.

A. At the 11​% level of​ significance, there issufficient evidence to support the claim that the mean credit card debt is less than ​$5,000.

B. At the 11​% level of​ significance, there is sufficient evidence to support the claim that the mean credit card debt is greater than$5,000.

C. At the 11​% level of​ significance, there is not sufficient evidence to support the claim that the mean credit card debt is less than $5,000.

D. At the 11​% level of​ significance, there is not sufficient evidence to support the claim that the mean credit card debt is greater than ​$5,000.

Answer 1