Question

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a​ two-candidate election, if a specific candidate receives at least 53 ​% of the vote in the​ sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters.

Answer 1

To estimate the proportion of college students who voted in the 2012 presidential election with 95 percent confidence and a margin of error no greater than 5 percent, a sample size of 385 students would be needed.

Step-by-step explanation:

To estimate the true proportion of college students on your campus who voted in the 2012 presidential election with 95 percent confidence and a margin of error no greater than 5 percent, you need to determine the sample size required for the survey. The formula to calculate the sample size is:

Sample Size = (Z^2 * p * (1 - p)) / E^2

Where:

• Z is the z-score for the desired confidence level (in this case, 95 percent confidence corresponds to a z-score of approximately 1.96)
• p is the estimated proportion of college students who voted in the election (which we don't know yet)
• E is the desired margin of error (in this case, 5 percent corresponds to 0.05)

Since we don't know the estimated proportion of college students who voted in the election, we can assume a worst-case scenario where p = 0.5, which maximizes the sample size. Substituting the values into the formula:

Sample Size = (1.96^2 * 0.5 * (1 - 0.5)) / 0.05^2

Sample Size = 384.16

Rounding up to the nearest whole number, you would need to interview at least 385 students to estimate the true proportion with the desired confidence and margin of error.