Question

In studying his campaign plans, Mr. Singleton wishes to estimate the difference between men's and women's...

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

Homework Answers

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)

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