Question

Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. Historically 24​% 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 160 people was chosen. From this​ sample, 51 people had credit scores less than 600. Using alpha=.05​, complete parts a and b below.

A.) H0=? H1=?

Critical Values of the test statistic?

Calculate the test statistic?

Reject or do not reject based on evidence of credit score level?

B.) P-Value?

Answer 1

A) we have to test if the persons have credit score less than 600 has increased after the crisis, so:

H0 : p^ <= P0  (the proportion of people having credit score less than 600 has not increased )

H1: p^ > P0 ((the proportion of people having credit score less than 600 has increased )

p^ = probability of having a credit having a credit score below 600 from a sample = 51/160 = 0.310875

P0 = historically 24% have a credit score below 600, = 0.24

n = 160; alpha = 0.05

critical value of the test statistic is 1.645 ( lokking the value from the z table)

Test statistic = (0.31-0.24)/ SQRT [0.24 * (1-0.24)]/ 160

= 0.07/ 0.033764 = 2.073

If test staistic > critical value , reject null hypothesis

Therefore we reject the null hypothesis and conclude that proportion of people having credit score less than 600 has increased after the crisis.

..

B) p-value is the probability of commiting type 1 error, type 1 error is rejecting true null hypothesis

p value: P(z>2.073) = 0.9808, therefore the p value is (1- 0.9808) = 0.0192