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 98% confidence interval for the difference. A random sample of 653 male voters and 560 female voters was taken. 226 men and 271 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.

Step 2 of 3:

Find the margin of error. Round your answer to six decimal places.

Step 3 of 3:

Construct the 98% confidence interval. Round your answers to three decimal places.

Answer 1

1)

Sample proportion 1 = 226 / 653 = 0.346

Sample proportion 1 = 271 / 560 = 0.484

Point estimate = 1 - 2 = 0.346 - 0.484 = -0.138

2)

Pooled proportion = (x1 + x2) / (n1 + n2)

= (226 + 271) / (653 + 560)

= 0.410

Margin of error = Z/2 * sqrt [ ( 1 - ) * ( 1 / n1 + 1/n2) ]

= 2.3263 * sqrt [ 0.410 * ( 1 - 0.410) * ( 1 / 653 + 1 / 560) ]

= 0.065897

3)

98% confidence interval for p is

1 - 2 - ME < p1 - p2 < 1 - 2 + ME

-0.138 - 0.065897 < p1 - p2 < -0.138 + 0.065897

-0.204 < p1 - p2 < -0.072

98% CI is ( -0.204 , -0.072 )