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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

1818

residents has a mean annual income of

$ 40 comma 100$40,100

and a standard deviation of

$ 8900$8900.

In County B, a random sample of

88

residents has a mean annual income of

$ 39 comma 000$39,000

and a standard deviation of

$ 5200$5200.

At

alphaαequals=0.100.10 ,

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

Upper H 0H0

and

Upper H Subscript aHa.

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 income in county A is less than in county B."

D.

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

What are

Upper H 0H0

and

Upper H Subscript aHa ?

The null hypothesis,

Upper H 0H0 ,

is

▼

mu 1 equals mu 2μ1=μ2

mu 1 less than or equals mu 2μ1≤μ2

mu 1 greater than or equals mu 2μ1≥μ2

. The alternative hypothesis,

Upper H Subscript aHa ,

is

▼

mu 1 not equals mu 2μ1≠μ2

mu 1 greater than mu 2μ1>μ2

mu 1 less than mu 2μ1<μ2

.

Which hypothesis is the claim?

The null hypothesis, Upper H 0H0

The alternative hypothesis, Upper H Subscript aHa

(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 less than minus t 0t<−t0

B.

t greater than t 0t>t0

C.

negative t 0 less than t less than t 0−t0<t<t0

D.

t less than minus t 0 comma t greater than t 0t<−t0, t>t0

(c) Find the standardized test statistic.

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

10 %10%

significance level,

▼

there is not

there is

enough evidence to support the personnel director's claim.

Answer 1