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 99% confidence interval for the difference. A random sample of 519 male voters and 587 female voters was taken. 237 men and 298 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 99% confidence interval. Round your answers to three decimal places.

Answer 1

solution:-

here n1 =519 , n2 = 587

step 1 of 4:

given that

male voters p1 = 237/519 = 0.457

female voters p2 = 298/587 = 0.508

step 2 of 4:

the 99% confidence from z critical value table is z = 2.576

step 3 of 4:

standard error

formula

=> sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

=> sqrt((0.457*(1-0.457)/519) + (0.508*(1-0.508)/587))

=> 0.030

Step 4 of 4:

the 99% confidence interval

=> (p1-p2) +/- z critical value * standard error

=> (0.457-0.508) +/- 2.576 * 0.030

=> (-0.128 , 0.026)