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 12 residents has a mean annual income of $40,300 and a standard deviation of $ 8900 In County B, a random sample of 10 residents has a mean annual income of $39,900 and a standard deviation of $5100. At alphaαequals=0.005, 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 less 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 greater than in county B." What are H0 and Ha? The null hypothesis, H0, is ▼ μ1=μ2 μ1≤μ2 μ1≥μ2 . The alternative hypothesis, Ha, is ▼ μ1≠μ2 μ1>μ2 μ1<μ2 . Which hypothesis is the claim? The alternative hypothesis, Ha The null hypothesis, H0 (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. nothing (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 B. t<−t0, t>t0 C. t<−t0 D. −t0

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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

residents has a mean annual income of

$40,300

and a standard deviation of

$ 8900

In County B, a random sample of

residents has a mean annual income of

$39,900

and a standard deviation of

$5100.

alphaαequals=0.005,

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

and

Ha.

Which is the correct claim below?

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

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

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

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

What are

and

Ha?

The null hypothesis,

H0,

▼

μ1=μ2

μ1≤μ2

μ1≥μ2

The alternative hypothesis,

Ha,

▼

μ1≠μ2

μ1>μ2

μ1<μ2

Which hypothesis is the claim?

The alternative hypothesis, Ha

The null hypothesis, H0

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

Enter the critical value(s) below.

nothing

(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.

t>t0

t<−t0, t>t0

t<−t0

−t0<t<t0

tequals=nothing

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

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

▼

Fail to reject

Reject

the null hypothesis.

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

At the

0.5 %

significance level,

▼

there is not

there is

enough evidence to support the personnel director's claim.

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