Question
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
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.
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