Question

An employment information service claims the mean annual salary for senior level product engineers is

​$97 comma 00097,000.

The annual salaries​ (in dollars) for a random sample of

1616

senior level product engineers are shown in the table to the right. At

alphaαequals=0.010.01​,

test the claim that the mean salary is

​$97 comma 00097,000.

Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.

nbsp Bold Annual Salaries nbsp Annual Salaries

100100

​,607607

9696

​,370370

9393

​,507507

112112

​,661661

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8282

​,479479

7474

​,165165

7676

​,941941

8080

​,946946

102102

​,429429

7676

​,189189

103103

​,978978

103103

​,927927

9191

​,174174

8282

​,114114

8585

​,084084

110110

​,362362

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0 : nbspH0:	▼ muμ pp sigma squaredσ2 sigmaσ ▼ less than or equals≤ greater than> equals= not equals≠ less than< greater than or equals≥ nothing
Upper H Subscript a Baseline : nbspHa:	▼ sigma squaredσ2 pp sigmaσ muμ ▼ less than or equals≤ less than< equals= not equals≠ greater than> greater than or equals≥ nothing

​(Type integers or decimals. Do not​ round.)

The claim is the

▼

alternative

null

hypothesis.

​(b) Use technology to find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is/are

t 0t0equals=nothing .

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

Choose the graph which shows the rejection region.

A.

-4  0  4   t

t 0t0

t less than t 0t<t0

Edit Coordinates(0,0)

A graph labeled t less than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. A vertical line segment extends from the curve to the t-axis at a point labeled t 0, where t 0 is to the left of 0. The area under the curve to the left of t 0 is shaded.

B.

-4  0  4   t

t 0t0

t greater than t 0t>t0

Edit Coordinates(0,0)

A graph labeled t greater than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. A vertical line segment extends from the curve to the t-axis at a point labeled t 0, where t 0 is to the right of 0. The area under the curve to the right of t 0 is shaded.

C.

   0     -44t

negative t 0−t0

t 0t0

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

Edit Coordinates(0,0)

A graph labeled t less than negative t 0, t greater than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. Two vertical line segments extend from the curve to the t-axis at the points labeled negative t 0 and t 0, where t 0 is to the right of 0. The areas under the curve to the left of negative t 0 and to the right of t 0 are shaded.

D.

   0     -44t

negative t 0−t0

t 0t0

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

Edit Coordinates(0,0)

A graph labeled negative t 0 less than t less than t 0 has a horizontal t-axis labeled from negative 4 to 4 in increments of 4. A symmetric bell shaped t-distribution curve is above the t-axis and centered on 0. Two vertical line segments extend from the curve to the t-axis at the points labeled negative t 0 and t 0, where t 0 is to the right of 0. The area under the curve between negative t 0 and t 0 is shaded.

​(c) Find the standardized test​ statistic, t.

The standardized test statistic is

tequals=nothing .

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

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

▼

Fail to reject

Reject

Upper H 0H0

because the standardized test statistic

▼

is not

is

in the rejection region.

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

There

▼

is not

is

enough evidence at the

nothing ​%

level of significance to

▼

supportsupport

rejectreject

the claim that the mean annual salary for senior level product engineers is

▼

less than

equal to

less than or equal to

greater than

greater than or equal to

not equal to

​$nothing .

​(Type integers or decimals. Do not​ round.)

Answer 1