Question

Prior to a statewide senate​ election, three polls are conducted concerning a particular​ candidate's popularity. In the first​ poll, 740 of 1550 voters favor the candidate. In the second​ poll, 1285 of 2520 favor the candidate. In the third​ poll, 1799 of 3500 voters favor the candidate. Find​ 95% confidence intervals for the proportion of voters in favor of the candidate for all three polls. Discuss the​ candidate's prospects for victory based on these polls.

Answer 1

We know that the 95% confidence interval for population proportion is given by:

Confidence interval for 1st poll:

Confidence interval for 2nd poll:

Confidence interval for 3rd poll:

Since the proportion lies between 45% and 53%, so the candidate has a decent chance of winning.