a random sample of 55 rapid city people was taken Each perso

a random sample of 55 rapid city people was taken. Each person surveyed was asked the question, \"Do you approve of the job that Mayor Kooiker?\" Of those surveyed, 42 answered yes.

a) Using the traditional formula, construct a 95% confidence interval for the proportion of residents who approve of his hob preformance?

b) State whether you think the confidence interval constructed in part a) is valid.

c) Are we able to extrapolate the results to all Rapid City residents? Explain why or why not.

Solution

Given n=55, X=42,then p=X/n=42/55=0.7636, & q=1-p=1-0.7636=0.2364. Then 95% confidence interval for the proportion of residents who approve of his job performance is [p+-(1.96*((pq)/n))]=[0.7636+-(1.96*((0.7636*0.2364)/55))]=[0.7363+-(1.96*0.0573)]=[0.7636+-0.1123]=(0.6513,0.8759).

This confidence interval is true for the proportion of residents who approve of his job performance.