Final answer:
To estimate the true proportion of college students who voted with 95% confidence and a ≤5% margin of error, you must interview at least 385 students, using the formula for sample size in estimating a proportion.
Step-by-step explanation:
To determine the number of students you must interview to estimate the true proportion of college students on your campus who voted in the 2012 presidential election with 95% confidence and a margin of error of no greater than 5%, you can use the formula for sample size in estimating a proportion:
n = (Z^2 * p * (1-p)) / E^2
Where:
- Z is the Z-value for the desired confidence level (1.96 for 95% confidence)
- p is the estimated proportion of success (since we don't have a prior estimate, we use 0.5 for maximum variability)
- E is the desired margin of error (0.05 for 5% margin of error)
Plugging in the values:
n = (1.96^2 * 0.5 * 0.5) / 0.05^2
n = (3.8416 * 0.25) / 0.0025
n = 0.9604 / 0.0025
n = 384.16
Since you cannot interview a fraction of a person, you round up to the nearest whole number. Therefore, you need to interview at least 385 students to achieve your desired confidence and margin of error.