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 588 male voters and 545 female voters was taken. 273 men and 322 women favored Mr. Singleton as a candidate. Find this confidence interval. Step 3 of 4 : Find the value of the standard error. Round your answer to three decimal places

Answer 1

We need to construct the 90% confidence interval for the difference between population proportions p_1 - p_2 ​. We have been provided with the following information about the sample proportions:

Favorable Cases 1 (X1​) =	273
Sample Size 1 (N1​) =	5 88
Favorable Cases 2 (X2​) =	3 22
Sample Size 2 (N2​) =	5 45

The sample proportion 1 is computed as follows, based on the sample size N_1 = 588 and the number of favorable cases X_1 = 273 :

The sample proportion 2 is computed as follows, based on the sample size N_2 = 545 and the number of favorable cases X_2 = 322:

The critical value for α=0.1 is z_c = 1.645. The corresponding confidence interval is computed as shown below:

CI = (-0.175, -0.078)

Standard error = Margin of error / z_c

Margin of error = ( -0.078 + 0.175 )/2

Margin of error = 0.836

Standard error = 0.836/1.645

Standard error = 0.5082