Question

	Black	Hispanic	White
Pass	9	6	41
Fail	18	17	27

Use this data and a 0.05 significance level to test the claim that less than 58% of the minority candidates (Black and Hispanic candidates grouped together) pass the lieutenants exam.

Sample proportion, p-hat = A. 0.26

B. 0.17

C. 0.31

D. 0.62

Test Statistic, z = A. -3.27

B. -2.71

C. 1.12

D. 0.82

Critical z = A. -1.645

B. 1.645

C. -1.645, 1.645

D. -1.96, 1.96

P-Value = A. 0.001

B. 0.962

C. 0.051

D. 0.041

A. Reject the null hypothesis. There is sufficient evidence to show that less than 58% of minority candidates pass the lieutenants exam.

B. Reject the null hypothesis. There is insufficient evidence to show that less than 58% of minority candidates pass the lieutenants exam.

C. Fail to reject the null hypothesis. There is sufficient evidence to show that less than 58% of minority candidates pass the lieutenants exam.

D. Fail to reject the null hypothesis. There is insufficient evidence to show that less than 58% of minority candidates pass the lieutenants exam.

Answer 1

Following table shows the row total and column total:

	Black	Hispanic	White	Total
Pass	9	6	41	56
Fail	18	17	27	62
Total	27	23	68	118

Total number of black and Hispanic candidates is 27+23 = 50

Out of 50 minority candidates, 9+6 = 15 pass the exam so the sample proportion is

------------------------

Correct options (choosing best possible):

Sample proportion,

C. 0.31

Test Statistic, z = A. -3.27

Critical z = A. -1.645

P-Value = A. 0.001

A. Reject the null hypothesis. There is sufficient evidence to show that less than 58% of minority candidates pass the lieutenants exam.