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. Construct and interpret a​ 95% confidence interval for the difference in the proportion of individuals who earn more than 100K and less than 100K and answered​ "yes" to the question stated.

Lower bound is________

Upper bound is________

2. Interpret your interval. Convert the lower and upper bounds of the interval to percents rounded to 1 decimal​ place, if needed. (answer choices below)

A. We are​ 95% confident that there is no significant difference between the proportion of individuals who earn in excess of​ $100,000 and think that is morally wrong for unwed women to have children and that of the individuals who earn less than​ $100,000.

B. We are​ 95% confident that the proportion of individuals who think that it is morally wrong for unwed women to have children is greater for those who earn more than​ $100K per year as opposed to those who earn less than​ $100K per year by between __% to ___%.

C. There is a​ 95% chance that the individuals who earn in excess of​ $100,000 and the individuals who earn less than​ $100,000 would agree regarding the question stated.

D. We are​ 95% confident that the proportion of individuals who think that it is morally wrong for unwed women to ahve children is greater for those who earn less than​ $100K per year as opposed to those who earn more than​ $100K per year by between the ___% to __%.

Answer 1

Answer:

1.

Given,

p1 = x1/n1 = 712/1205 = 0.5909

p2 = x2/n2 = 690/1310 = 0.5267

Here at 95% CI, z value is 1.96

CI = (p1-p2) +/- z*sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

substitute values

= (0.5909 - 0.5267) +/- 1.96*sqrt(0.5909(1-0.5909)/1205 + 0.5267(1-0.5267)/1310)

= 0.0642 +/- 0.0388

= (0.0254 , 0.1030)

Upper bound = 0.1030

Lower bound = 0.0254

Here we are 95% confident that interval is from 0.0254 to 0.103.