Question

Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. Historically 23​% 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, 47 people had credit scores less than 600. Using α=0.05 complete parts a and b below.

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

b)Calculate the test statistic.

c)Determine the proper conclusion. Choose the correct answer below.

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

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

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

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

d) determine the p-value for this test

Answer 1

Here we will use the one-sample proportion test to check whether the proportion is increased or not.

Here X = Number of people in the sample having a credit score below 600 = 47

n = sample size = 160

We want to test

: = 0.23

vs

p > 0.23

a) SInce it is one-tail test and level of significance is 0.05 critical value is = 1.64

b) Now test statistic is

= X/n = 47/160 = 0.2938

= 0.23

So test statistic =  1.916

c) Here test statistic = 1.916 > 1.64 =crtical value So we reject Ho

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

d) p-value is 0.0277