Question

A politician claims that the mean salary for managers in his state is more than the national? mean, ?81,000. Assume the the population is normally distributed and the population standard deviation is ?$9000. The salaries? (in dollars) for a random sample of 30 managers in the state are listed. At ?=0.1?, is there enough evidence to support the? claim? Use technology

97,114
79,642
71,801
88,955
76,739
75,497
95,067
95,523
94,043
80,146
96,239
90,034
94,963
76,493
83,155
92,796
71,584
94,954
81,307
85,513
83,443
70,803
79,791
95,575
90,196
83,513
94,204
71,080
87,668
94,662

) Identify the null hypothesis and alternative hypothesis.

A.

Upper H 0H0?:

mu?not equals?81 comma 00081,000

Upper H Subscript aHa?:

mu?equals=81 comma 00081,000

B.

Upper H 0H0?:

mu?less than or equals?81 comma 00081,000

Upper H Subscript aHa?:

mu?greater than>81 comma 00081,000

C.

Upper H 0H0?:

mu?greater than>81 comma 00081,000

Upper H Subscript aHa?:

mu?less than or equals?81 comma 00081,000

D.

Upper H 0H0?:

mu?greater than or equals?81 comma 00081,000

Upper H Subscript aHa?:

mu?less than<81 comma 00081,000

E.

Upper H 0H0?:

mu?equals=81 comma 00081,000

Upper H Subscript aHa?:

mu?not equals?81 comma 00081,000

F.

Upper H 0H0?:

mu?greater than>81 comma 00081,000

Upper H Subscript aHa?:

mu?less than or equals?81 comma 00081,000

?(b) Identify the standardized test statistic.

zequals=nothing

?(Round the final answer to two places as needed. Round all intermediate values to three places as? needed.)

?(c) Find the? P-value. Use technology.

nothing

?(Round to three decimal places as? needed.)

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

A.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence to support the claim that managers mean salary is more than the national mean.

B.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence to support the claim that managers mean salary is more than the national mean.

C.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not??

sufficient evidence to support the claim that managers mean salary is more than the national mean.

D.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

sufficient evidence to support the claim that managers mean salary is more than the national mean.

Answer 1

We have given observations in increasing order will be,
70803,71080,71584,71801,75497,76493,76739,79642,79791,80146,81307,
83155,83443,83513,85513,87668,88955,90034,90196,92796,94043,94204,94662,
94954,94963,95067,95523,95575,96239,97114

Sample size:30

Mean (x?): 85750
Standard deviation (s): 8819.943

a)  the null hypothesis and alternative hypothesis.

Option B) is correct.

vs

?(b) the standardized test statistic.

=2.891

  

c) P value =0.002

?(d) Option A) is correct.

Reject H0.

There is sufficient evidence to support the claim that managers mean salary is more than the national mean.