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 643 male voters and 565 female voters was taken. 139 men and 199 women favored Mr. Singleton as a candidate. Find this confidence interval.

Step 2 of 4:

Find the critical value that should be used in constructing the confidence interval.

Find the value of the standard error. Round your answer to three decimal places.

Construct the 98% confidence interval. Round your answers to three decimal places. Lower and upper endpoint

Answer 1

Here, , n1 = 643 , n2 = 565
p1cap = X1/N1 = 139/643 = 0.2162
p2cap = X2/N2 = 199/565 = 0.3522

p1cap = 0.2162 , p2cap = 0.3522

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, Zc = Z(α/2) = 2.33

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.2162 * (1-0.2162)/643 + 0.3522*(1-0.3522)/565)
SE = 0.026

For 0.98 CI, z-value = 2.33
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.2162 - 0.3522 - 2.33*0.026, 0.2162 - 0.3522 + 2.33*0.026)
CI = (-0.197 , -0.075)