Question

A personnel director in a particular state claims that the mean annual income is greater in one of the​ state's counties​ (county A) than it is in another county​ (county B). In County​ A, a random sample of 13 residents has a mean annual income of $42,000 and a standard deviation of $8800. In County​ B, a random sample of 11 residents has a mean annual income of $37,700 and a standard deviation of $5700. At At alphaαequals= 0.025 answer parts​ (a) through​ (e). Assume the population variances are not equal. If​ convenient, use technology to solve the problem.

​(a) Identify the claim and state H0 and Ha.

Which is the correct claim​ below?

A. ​"The mean annual income in county A is greater than in county​ B."

B. "The mean annual incomes in counties A and B are not​ equal."

C. ​"The mean annual incomes in counties A and B are​ equal."

D. "The mean annual income in county A is less than in county​ B."

What are H0 and Ha​?

The null​ hypothesis, H0​, is____ . The alternative​ hypothesis, Ha​, is____

.Which hypothesis is the​ claim?

A. The null​ hypothesis, H0

b.The alternative​ hypothesis, Ha

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

Enter the critical​ value(s) below.

=

​(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.)

Select the correct rejection​ region(s) below.

A. t <− t0, t > t0

B. −t0 < t < t0

C. t> t0

D.  t < −t0

​(c) Find the standardized test statistic.

t = ​(Type an integer or decimal rounded to three decimal places as​ needed.)

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

A.Fail to reject

B.Reject

the null hypothesis.

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

At the 2.5% significance​ level,

A .there is not

B. there is

enough evidence to support the personnel​ director's claim

Answer 1