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 200 people was chosen. From this sample, 53 people had credit scores less than 600. Using a = 0.05, 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. O A. Ho:p>0.23 H:ps 0.23 B. Ho: p50.23 H:p>0.23 OD. Ho:p0.23 H, p<0.23 0C. Hp: p = 0.23 H:p*0.23 Determine the critical value(s) of the test statistic. Za = 1.645 (Use a comma to separate answers as needed. Round to three decimal places as needed.) Calculate the test statistic. Zo = 1.18 (Round to two decimal places as needed.) Determine the proper conclusion. Choose the correct answer below. A. Do not reject H. There is insufficient evidence that the proportion of people with credit scores below 600 has increased. OB. Reject H. There is insufficient evidence that the proportion of people with credit scores below 600 has increased. O C. Do not reject H. There is sufficient evidence that the proportion of people with credit scores below 600 has increased. XD. Reject H. There is sufficient evidence that the proportion of people with credit scores below 600 has increased. b. Determine the p-value for this test. p-value = 0.120 (Round to three decimal places as needed.)

Answer 1

Given: population proportion (p = 23%. = 0.23 Sample size (n) = 200 2 Selected sample (X) = 53 Level of significance (x) = 0.05 Ho: Hip P < 0.23 > 0.23 Tall 130 Determine crtical z value of the test Statistic using a table, look in to a 50.05 value in the body of the table for right tail test we get Za = 7.645 in 20 V7 Zx = 1.645 - calculate T test statistic ê - i - 1 Where, - 53 200 - 10.265 0.265 - 0,23 0 23. (170-23) 0.035 1.176 0.029757352 ñ 1.181 crounding to 2 decimal) I Decision Rule : If a test statishic. Value lie in shaded If test statishic. zvalue lie in Unshased region then do not reject region then njeet Ho 1.645

Since, z test statistic F118 unshaded region (ie less than zintical valve) I statistic = 118 is lie in region Cie z test statistic is s Therefore, we do not reject to Do not reject Ho There is insufficient evidence that the proportion of people with credit scores below 6oo has increased p value dit Determine the P value when > Ha contains sign P value = ' P < Z test statistich hi tost tohoto > - P(Z < 1018 => ) - 0.8810 By Z Using z table 0.0o..... 10.08 )ะกๆ 1 z table > Oollg > 108810 1.0.8810 . p value = 10.119 v