Question

Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. Historically 29​% of people had a credit score below 600. Due to the recent financial​ crisis, the federal government is concerned that this proportion has increased. To test this​ hypothesis, a random sample of 500 people was chosen. From this​ sample, 170 people had credit scores less than 600. Using alpha=0.10​, complete parts a and b below.

a. Does this sample provide support for the​ government's concern that the proportion of people with credit scores below 600 has​ increased?

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

A.

H0​: π≥0.29

H1​:π<0.29

B.

H0​:π>0.29

H1​: π≤0.29

C.

H0​: π=0.29

H1​: π≠0.29

D.

H0​: π≤0.29

H1​: π>0.29

Determine the critical​ value(s) of the test statistic. ____

​(Use a comma to separate answers as needed. Round to

two decimal places as​ needed.)

Calculate the test statistic.

_____

​(Round to two decimal places as​ needed.)

Determine the proper conclusion. Choose the correct answer below.

A.

Do not reject H0. There is insufficient evidence that the proportion of people with credit scores below 600 has increased.

B.

Reject H0. There is sufficient evidence that the proportion of people with credit scores below 600 has increased.

C.

Reject H0. There is insufficient evidence that the proportion of people with credit scores below 600 has increased.

D.

Do not reject H0. There is sufficient evidence that the proportion of people with credit scores below 600 has increased.

b. Determine the​ p-value for this test.

______

​(Round to three decimal places as​ needed.)

Answer 1