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 the1,205 individuals who earned in excess of​ $100,000 per​ year, 712712 said​ yes; of the 1,310 individuals who earned less than​ $100,000 per​ year, 690690 said yes. Construct a​ 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.

The lower bound is ?.

The upper bound is ?.

​(Round to three decimal places as​ needed.)

Because the confidence interval -includes/does not include- ​0, there is -insufficient/sufficient- evidence at the alpha=0.05 level of significance to conclude that there is a difference in the proportions. It seems that the proportion of individuals who earn over​ $100,000 that feel it is morally wrong for unwed women to have children is -not different/different/greater than- the proportion of individuals who earn less than​ $100,000 that feel it is morally wrong for unwed women to have children.

Answer 1

Answer:

n1= 1205, x1= 712

n2= 1310, x2= 690

c= 95%,

0.5909

0.5267

formula for confidence interval is

Where Zc is the z critical value for c=95%

Zc= 1.96

0.0254 < P1 - P2 < 0.10291

The lower bound is = 0.025

The upper bound is = 0.103

Because the confidence interval -does not include- ​0, there is -sufficient- evidence at the alpha=0.05 level of significance to conclude that there is a difference in the proportions. It seems that the proportion of individuals who earn over​ $100,000 that feel it is morally wrong for unwed women to have children is -different than- the proportion of individuals who earn less than​ $100,000 that feel it is morally wrong for unwed women to have children.