Question

Brandon and Joy are the final candidates for the president of the class of 143 students. To find their chances of winning the election, each conducted a survey. The results of both surveys, as well as the manner in which they were obtained, are:

a) Brandon's survey showed 78% in favor of him.
b) Joy's survey showed 64% in favor of her.
c) Brandon's survey was obtained through online polls.
d) Joy's survey was obtained through in-person interviews

Answer 1

To estimate the true proportion of college students who voted in the 2012 presidential election with 95% confidence and a margin of error no greater than 5%, you need to determine the sample size.

Step-by-step explanation:

To estimate the true proportion of college students who voted in the 2012 presidential election with 95% confidence and a margin of error no greater than 5%, you need to determine the sample size. The margin of error is the range in which the true proportion is likely to fall. In this case, the margin of error is 5%, which means the true proportion could be 5% higher or lower than the observed proportion in the sample. The formula to calculate the required sample size is:

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

where:

• n is the required sample size
• Z is the Z-score corresponding to the desired confidence level (Z = 1.96 for 95% confidence)
• p is the estimated proportion from the sample (0.5 for maximum variability)
• E is the desired margin of error (0.05 for 5%)

Plugging in the values, we get:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.05^2) = 384.16

Rounding up to the nearest whole number, you would need to interview at least 385 students to estimate the true proportion of college students who voted in the 2012 presidential election with 95% confidence and a margin of error no greater than 5%.