According to data only

31%

of Americans are saving for retirement in a 401(k). A random sample of

340

Americans was recently selected, and it was found that

118

of them made contributions to their 401(k) plans this year. Using

=0.01,

complete parts a through c.

a. Using

=

0.01,

perform a hypothesis test to determine if the percentage of Americans who have made contributions to their 401(k) plan is more than

31%.

Let p be the population proportion. Determine the null hypothesis,

H0,

and the alternative hypothesis,

H1.

H0:

p

equals=

not equals

greater than or equals

less than or equals

H1:

p

less than<

greater than>

not equals

equals=

(Type integers or decimals. Do not round.)

b. Determine the p-value for this test and interpret its meaning.

Identify the critical value.

negative z Subscript alpha divided by 2z/2

t Subscript alpha divided by 2t/2

negative z Subscript alphaz

t Subscript alphat

z Subscript alpha divided by 2z/2

negative t Subscript alpha divided by 2t/2

negative t Subscript alphat

z Subscript alphaz

=

(Round to two decimal places as needed.)

Calculate the appropriate test statistic.

zp=

(Round to two decimal places as needed.)

Determine the p-value for this test and interpret its meaning.

p-value=

(Round to three decimal places as needed.)

Interpret the meaning of the p-value. Choose the correct answer below.

A.

Reject

H0.

There

is

enough evidence to conclude that the percentage of employees who have made contributions to their 401(k) plan is more than

31%.

B.

Reject

H0.

There

isnot

enough evidence to conclude that the percentage of employees who have made contributions to their 401(k) plan is more than

31%.

C.

Donotreject

H0.

There

is

enough evidence to conclude that the percentage of employees who have made contributions to their 401(k) plan is more than

31%.

D.

Donotreject

H0.

There

isnot

enough evidence to conclude that the percentage of employees who have made contributions to their 401(k) plan is more than

31%.

c. How would the conclusions be affected if you chose to use

=

0.05

rather than

=

0.01?

Choose the correct answer below.

A.

Using

=

0.05

rather than

=

0.01

does change the conclusion in this case. Increasing the value of

increases the likelihood of rejecting the null hypothesis.

B.

Using

=

0.05

rather than

=

0.01

does change the conclusion in this case. Increasing the value of

decreases the likelihood of rejecting the null hypothesis.

C.

Using

=

0.05

rather than

=

0.01

does not change the conclusion in this case. But increasing the value of

increases the likelihood of rejecting the null hypothesis.

D.

Using

=

0.05

rather than

=

0.01

does not change the conclusion in this case. But increasing the value of

decreases the likelihood of rejecting the null hypothesis.