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 517 male voters and 529 female voters was taken. 194 men and 148 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.

Step 3 of 4: Find the value of the standard value

Answer 1

The statistic software output for this problem is:

Two sample proportion summary hypothesis test: P1 proportion of successes for population 1 P2 proportion of successes for population 2 P1- P2 Difference in proportions Ho P1 - P2 0 HA P1- P2 0 Hypothesis test results: Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err P-value Z-Stat 517 529 148 194 0.21442909 0.022799586 9.4049553 <0.0001 P1-P2

1)

pˆ1 =  517 / 529 = 0.977

and pˆ2 = 148/194 = 0.763

2) Critical value = +/-1.645

3) Test statistic = 9.405