Question

Test the claim about the population mean,

muμ ,

at the given level of significance using the given sample statistics. Claim:

muμequals=4040 ;

alphaαequals=0.060.06 ;

sigmaσequals=3.873.87.

Sample statistics:

x overbarxequals=38.738.7 ,

nequals=7676

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμgreater than>4040

B.

Upper H 0H0 :

muμgreater than>4040

Upper H Subscript aHa :

muμequals=4040

C.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμnot equals≠4040

D.

Upper H 0H0 :

muμequals=4040

Upper H Subscript aHa :

muμless than<4040

E.

Upper H 0H0 :

muμless than<4040

Upper H Subscript aHa :

muμequals=4040

F.

Upper H 0H0 :

muμnot equals≠4040

Upper H Subscript aHa :

muμequals=4040

Calculate the standardized test statistic.

The standardized test statistic is

nothing .

(Round to two decimal places as needed.)

Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice.

(Round to two decimal places as needed.)

A.

The critical values are

plus or minus±nothing .

B.

The critical value is

nothing .

Determine the outcome and conclusion of the test. Choose the correct answer below.

A.

Fail to rejectFail to reject

Upper H 0H0.

At the

66 %

significance level, there

is notis not

enough evidence to reject the claim.

B.

Fail to rejectFail to reject

Upper H 0H0.

At the

66 %

significance level, there

is notis not

enough evidence to support the claim.

C.

RejectReject

Upper H 0H0.

At the

66 %

significance level, there

isis

enough evidence to reject the claim.

D.

RejectReject

Upper H 0H0.

At the

66 %

significance level, there

isis

enough evidence to support the claim.

Answer 1

Solution:

Given:

Claim:

α = 0.06 ;

σ =3.87

Sample statistics:

=38.7  

n =76

Part a) Identify the null and alternative hypotheses.

Since claim is non-directional this is two tailed test.

thus

C.

H0 : μ =40

Ha : μ ≠ 40

Part b) Calculate the standardized test statistic.

Part c) Determine the critical value(s).

Since this is two tailed test and level of significance = = 0.06

Find

Look in z  table for Area = 0.0300 or its closest area and find corresponding z value.

Area 0.0301 is closest to 0.0300 and it corresponds to -1.8 and 0.08
that is  z = -1.88

Thus z critical values : ( -1.88 , 1.88)

that is:  ± 1.88

Part d) Determine the outcome and conclusion of the test.

Since z test statistic value = -2.93 < -1.88, we reject H0.

C. Reject H0. At the 6 % significance level, there is enough evidence to reject the claim.