Question

In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men's and women's views regarding his appeal as a candidate. He asks his campaign manager to take two random independent samples and find the 99% confidence interval for the difference. A random sample of 672 male voters and 698 female voters was taken. 319 men and 212 women favored Mr. Singleton as a candidate. Find this confidence interval. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places. Find the margin of error. Round your answer to six decimal places. Construct the 99% confidence interval. Round your answers to three decimal places.

Answer 1

Values are given as,

z= 2.575 (critical value of 99%)

n1 = 672 , x1 = 319	= (x/n) = (319/672) = 0.475
n2 = 698 , x2 = 212	= (x/n)= (212/698) = 0.304

The point estimate :

Calculating margin of error for 99% confidence interval :

Using the formula;

Putting the values :

E= 45.721000

The margin of error : E= 45.721000

Calculating 99% confidence interval :

CI= -45.550 , 45.892

The 99% confidence interval : ( -45.550 <<  45.892)