A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x overbarxequals=5.25.2,

sequals=1.41.4.

Complete parts a through c.

a. Test the null hypothesis that the mean of the population is 66

against the alternative hypothesis, muless than<66.

Use alphaequals=0.050.05.

If alphaequals=0.050.05,

find the rejection region for the test. Choose the correct answer below.

A.

tless than2.7762.776

B.

tless than2.1322.132

or tgreater than>2.1322.132

C.

tgreater than>2.7762.776

D.

tgreater than>2.1322.132

E.

tless than2.7762.776

or tgreater than>2.7762.776

F.

tless than2.1322.132

Calculate the value of the test statistic.

tequals=nothing

(Round to two decimal places as needed.)

Make the appropriate conclusion. Choose the correct answer below.

A.

RejectReject

H0.

There is insufficientinsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is less than 66.

B.

Do not rejectDonotreject

H0.

There is sufficientsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is less than 66.

C.

Do not rejectDonotreject

H0.

There is insufficientinsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is less than 66.

D.

RejectReject

H0.

There is sufficientsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is less than 66.

b. Test the null hypothesis that the mean of the population is 66

against the alternative hypothesis, munot equals66.

Use alphaequals=0.050.05.

If alphaequals=0.050.05,

find the rejection region for the test. Choose the correct answer below.

A.

tless than2.1322.132

B.

tless than2.7762.776

C.

tless than2.1322.132

or tgreater than>2.1322.132

D.

tgreater than>2.7762.776

E.

tgreater than>2.1322.132

F.

tless than2.7762.776

or tgreater than>2.7762.776

Calculate the value of the test statistic.

tequals=nothing

(Round to two decimal places as needed.)

Make the appropriate conclusion. Choose the correct answer below.

A.

Do not rejectDonotreject

H0.

There is sufficientsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is not 66.

B.

Do not rejectDonotreject

H0.

There is insufficientinsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is not 66.

C.

RejectReject

H0.

There is sufficientsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is not 66.

D.

RejectReject

H0.

There is insufficientinsufficient

evidence at the alphaequals=0.050.05

level of significance to conclude that the true mean of the population is not 66.

c. Find the observed significance level for each test.

Find the observed significance level for the test in part a.

p-valueequals=nothing

(Round to three decimal places as needed.)

Find the observed significance level for the test in part b.

p-valueequals=nothing

(Round to three decimal places as needed.)