Question

incorrect, Instructor-created question

The research group asked the following question of individuals who earned in excess of​ $100,000 per year and those who earned less than​ $100,000 per​ year: "Do you believe that it is morally wrong for unwed women to have​ children?" Of the 1,205 individuals who earned in excess of​ $100,000 per​ year, 712 said​ yes; of the 1,310 individuals who earned less than​ $100,000 per​ year, 690 said yes.

1. Compute the test statistic (4 decimal places) and the P-value (3 decimal places).

2. Write the conclusion to the hypothesis testing in the context of the problem using​ P-value approach with the level of significance alpha equals 0.05 (below are option A to D)

A.We have enough evidence to conclude that the proportion of individuals who believe that is morally wrong for unwed women to have children is greater for people who earn in excess of​ $100K as compared to people who earn less than​ $100K.

B. We do not have enough evidence to conclude that the proportion of individuals who believe that it is morally wrong for unwed women to have children is different for people who earn in excess of​ $100K as compared to people who earn less than​ $100K.

C.We have enough evidence to conclude that the proportion of individuals who believe that is morally wrong for unwed women to have children is less for people who earn in excess of​ $100K as compared to people who earn less than​ $100K.

D. We have enough evidence to conclude that the proportion of individuals who believe that it is morally wrong for unwed women to have children is different for people who earn in excess of​ $100K as compared to people who earn less than​ $100K.

Answer 1

Test statistic

Z = (p1-p2) / sqrt(p(1-p)(1/n1+1/n2))

Where p = (n1*p1 + n2*p2) / (n1+n2)

= (712+690)/(1205+1310)

= 1402/2515

= 0.56

Z = (0.59-0.53)/ sqrt(0.56*0.44(0.0008+0.0007))

= 0.06/ 0.019

= 3.157

P value corresponding to z = 3.157 of one tailed test is 0.000797

Since p value is less than 0.05, we conclude that

A. We have enough evidence to conclude that the proportion of individuals who believe that it is morally wrong for unwed women to have children is greater for people who earn in excess of $100k as compared to people who earn less than $100k