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 100 people was chosen. From this​ sample, 28 people had credit scores less than 600. Using alphaαequals=0.05​, complete the following:

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.

b.)

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

z Subscript alphazαequals = ___

Answer 1

Given that, n = 100 and x = 28

=> sample proportion = 28/100 = 0.28

a) The null and alternative hypotheses are,

H0 : p = 0.23

Ha : p > 0.23

This test is right-tailed test.

b) critical value at significance level of 0.05 is, Z^* = 1.645

=> Zα = 1.645

c) Test statistic is,

=> Test statistic = Z = 1.19

Since, test statistic = 1.19 < 1.645, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to support for the​ government's concern that the proportion of people with credit scores below 600 has​ increased.