Question

Is the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $8000? To​ decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At α=0.10, what should you​ conclude? Answer A-E

Region 1

x1 = $68,300

standard deviation = $8,750

n1 = 47

Region 2

x2 = $63,000

standard deviation = $9,275

n2 = 40

A. What are the alternative and null hypotheses? Express them mathematically.

B. Determine the critical values and rejection regions

C. Calculate the standardized test statistic

D. Choose the correct answer below

a) Fail to reject H null, at the​ 1% significance​ level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

b) Reject H null, at the​ 1% significance​ level, there is sufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

c) Reject H null, at the​ 1% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

d) Fail to reject H null, at the​ 1% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

Answer 1

Conclusion :

d) Fail to reject H null, at the​ 10% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000

If

Conclusion :

d) Fail to reject H null, at the​ 1% significance​ level, there is insufficient evidence to support the claim that the difference between the mean annual salaries is more than ​$8000