Question

An employment information service claims the mean annual pay for​ full-time male workers over age 25 without a high school diploma is

​$22 comma 35022,350.

The annual pay for a random sample of

1010

​full-time male workers over age 25 without a high school diploma is listed. At

alphaαequals=0.010.01​,

test the claim that the mean salary is

​$22 comma 35022,350.

Assume the population is normally distributed.

20 comma 65520,655

21 comma 13421,134

22 comma 35822,358

21 comma 39521,395

22 comma 97122,971

16 comma 91116,911

19 comma 15419,154

23 comma 19923,199

24 comma 18624,186

26 comma 28126,281

​(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

muμequals=22 comma 35022,350

Upper H Subscript aHa​:

muμgreater than>22 comma 35022,350

B.

Upper H 0H0​:

muμequals=22 comma 35022,350

Upper H Subscript aHa​:

muμnot equals≠22 comma 35022,350

C.

Upper H 0H0​:

muμequals=22 comma 35022,350

Upper H Subscript aHa​:

muμless than<22 comma 35022,350

D.

Upper H 0H0​:

muμnot equals≠22 comma 35022,350

Upper H Subscript aHa​:

muμequals=22 comma 35022,350

E.

Upper H 0H0​:

muμgreater than or equals≥22 comma 35022,350

Upper H Subscript aHa​:

muμless than<22 comma 35022,350

F.

Upper H 0H0​:

muμgreater than>22 comma 35022,350

Upper H Subscript aHa​:

muμless than or equals≤22 comma 35022,350

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

What​ is(are) the critical​ value(s),

t 0t0​?

t 0t0equals=nothing

​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

Which of the following graphs best depicts the rejection region for this​ problem?

A.0

nbsp t 0  t0

A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at t@Sub{0}, where t@Sub{0} is to the left of 0. The area under the curve to the left of t@Sub{0} is shaded.

B.0

nbsp t 0  t0

A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at t@Sub{0}, where t@Sub{0} is to the right of 0. The area under the curve to the right of t@Sub{0} is shaded.

C.0

nbsp t 0  t0

negative t 0−t0

A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative t@Sub{0}, 0 and t@Sub{0}, where negative t@Sub{0} is to the left of 0 and t@Sub{0} is to the right of 0. The area under the curve to the left of negative t@Sub{0} and to the right of t@Sub{0} is shaded.

​(c) Find the standardized test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

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

A.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

B.

RejectReject

Upper H 0H0

because the test statistic

isis

in the rejection region.

C.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

isis

in the rejection region.

D.

RejectReject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

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

A.There

is notis not

sufficient evidence to reject the claim that the mean salary is $ 22 comma 350.$22,350.

B.There

isis

sufficient evidence to reject the claim that the mean salary is not $ 22 comma 350.$22,350.

C.There

isis

sufficient evidence to reject the claim that the mean salary is $ 22 comma 350.$22,350.

D.There

is notis not

sufficient evidence to reject the claim that the mean salary is not $ 22 comma 350.

Answer 1