In April 2010,

44%

of the unemployed had been out of work longer than six months. Policy makers felt that this percentage declined during 2010 as the job market improved. To test this theory, a random sample of

400

unemployed people was selected, and it was found that

161

had been out of work for more than six months. Using

=0.10,

answer parts a through c below.

a. calculate test statics

round to two place as needed.

Determine the conclusion. Choose the correct answer below.

A.

Donotreject

H0.

There

is

sufficient evidence to conclude that the proportion of the unemployed who have been out of work for more than six months declined during 2010.

B.

Donotreject

H0.

There

isnot

sufficient evidence to conclude that the proportion of the unemployed who have been out of work for more than six months declined during 2010.

Your answer is not correct.

C.

Reject

H0.

There

isnot

sufficient evidence to conclude that the proportion of the unemployed who have been out of work for more than six months declined during 2010.

D.

Reject

H0.

There

is

sufficient evidence to conclude that the proportion of the unemployed who have been out of work for more than six months declined during 2010.

b.Determine the p-value for this test.

p-value=enter your response here

(Round to three decimal places as needed.)

c. Comment on the value of

selected for this test. Choose the correct answer below.

A.

The value of

selected for this test is a commonly used value of

and is appropriate for any test.

B.

If the policy makers felt it was critical that they didn't make a Type II error, then it would have been better to select a lower value of

for the test.

C.

If the policy makers felt it was critical that they didn't make a Type I error, then it would have been better to select a lower value of

for the test.

D.

If the policy makers felt it was critical that they didn't make a Type I error, then it would have been better to select a higher value of

for the test.