Question

An employment information service claims the mean annual pay for​ full-time male workers over age 25 without a high school diploma is ​$22,300. The annual pay for a random sample of 10 ​full-time male workers over age 25 without a high school diploma is listed. At α=0.05, test the claim that the mean salary is ​$22,300. Assume the population is normally distributed.

20,657   21,133   22,356 21,393 22,978 16,915 19,152 23,192 24,188 26,280

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

Which of the following correctly states H0 and Ha​?

A. H0​: μ = 22,300

Ha​: μ < 22,300

B.H0​: μ = 22,300

Ha​: μ > 22,300

C. H0​: μ ≠ 22,300

Ha​: μ = 22,300

D. H0​: μ > 22,300

Ha​: μ ≤ 22,300

E. H0​: μ ≥ 22,300

Ha​: μ < 22,300

F. H0​: μ = 22,300

Ha​: μ ≠ 22,300

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

What​ is(are) the critical​ value(s), t 0t0​?

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

(c) Find the standardized test statistic.

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

​

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

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

B. Fail to reject H0 because the test statistic is in the rejection region.

C. Reject H0 because the test statistic is not in the rejection region.

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

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

A.There is sufficient evidence to reject the claim that the mean salary is $22,300.

B.There is not sufficient evidence to reject the claim that the mean salary is not $22,300

C.There is sufficient evidence to reject the claim that the mean salary is not $ 22,300.

D.There is not sufficient evidence to reject the claim that the mean salary is $22,300.

Answer 1