# A personnel director in a particular state claims that the mean annual income is the same in one of the​ state's counties​ (County A) as it is in another county​ (County B). In County​ A, a random sample of 17 residents has a mean annual income of $42,100 and a standard deviation of$8300.In County​ B, a random sample of 14 residents has a mean annual income of $37,900 and a standard deviation of$5700. At α=0.05, answer parts​ (a) through​ (e). Assume the population variances are not equal. Assume the samples are random and​ independent, and the populations are normally distributed. ​(a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa.   Which is the correct claim​ below?   A. ​"The mean annual incomes in Counties A and B are not​ equal."   B. ​"The mean annual incomes in Counties A and B are​ equal." This is the correct answer.   C. ​"The mean annual income in County A is greater than in County​ B."   D. ​"The mean annual income in County A is less than in County​ B." What are Upper H 0H0and Upper H Subscript aHa​?   The null​ hypothesis, Upper H 0H0​, is mu 1 equals mu 2 .μ1=μ2.   The alternative​ hypothesis, Upper H Subscript aHa​, is mu 1 not equals mu 2 .μ1≠μ2.   Which hypothesis is the​ claim?     The alternative​ hypothesis, Upper H Subscript aHa   The null​ hypothesis, Upper H 0H0 Your answer is correct. ​(b) Find the critical​ value(s) and identify the rejection​ region(s).   Enter the critical​ value(s) below.

Question
A personnel director in a particular state claims that the mean annual income is the same in one of the​ state's counties​ (County A) as it is in another county​ (County B). In County​ A, a random sample of 17 residents has a mean annual income of $42,100 and a standard deviation of$8300.
In County​ B, a random sample of 14 residents has a mean annual income of
$37,900 and a standard deviation of$5700. At α=0.05,
answer parts​ (a) through​ (e). Assume the population variances are not equal. Assume the samples are random and​ independent, and the populations are normally distributed.
​(a) Identify the claim and state
Upper H 0H0
and
Upper H Subscript aHa.

Which is the correct claim​ below?

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

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

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

D.
​"The mean annual income in County A is less than in County​ B."
What are Upper H 0H0
and Upper H Subscript aHa​?

The null​ hypothesis,
Upper H 0H0​,
is
mu 1 equals mu 2 .μ1=μ2.

The alternative​ hypothesis,
Upper H Subscript aHa​,
is
mu 1 not equals mu 2 .μ1≠μ2.

Which hypothesis is the​ claim?

The alternative​ hypothesis, Upper H Subscript aHa

The null​ hypothesis, Upper H 0H0
​(b) Find the critical​ value(s) and identify the rejection​ region(s).

Enter the critical​ value(s) below.