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 90% confidence interval for the difference. A random sample of 526 male voters and 576 female voters was taken. 223 men and 197 women favored Mr. Singleton as a candidate. Find this confidence interval.

Step 1 of 4: Find the values of the two sample proportions, pˆ1 and pˆ2. Round your answers to three decimal places.

Step 2 of 4: Find the critical value that should be used in constructing the confidence interval.

Step 3 of 4: Find the value of the standard error. Round your answer to three decimal places.

Step 4 of 4: Construct the 90%90% confidence interval. Round your answers to three decimal places.

Answer 1

1)
Here, , n1 = 526 , n2 = 576
p1cap = 0.424 , p2cap = 0.342

2)
For 0.9 CI, z-value = 1.64

3)

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.424 * (1-0.424)/526 + 0.342*(1-0.342)/576)
SE = 0.029

4)

Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.424 - 0.342 - 1.64*0.029, 0.424 - 0.342 + 1.64*0.029)
CI = (0.034 , 0.13)