1. As in Exercise 9, you want to estimate the proportion of traditional college students on your campus who own their own car. However, from some research on other college campuses, you believe the proportion will be near 20%.
a) What sample size is needed if you wish to be 95% confi- dent that your estimate is within 0.02 of the true proportion?
b) What sample size is needed if you wish to be 99% confi- dent that your estimate is within 0.02 of the true proportion?
c) What sample size is needed if you wish to be 95% confi- dent that your estimate is within 0.05 of the true proportion?
2. It's believed that as many as 25% of adults over age 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.
a) How many of this younger age group must we survey in order to estimate the proportion of nongrads to within 6% with 90% confidence?
b) Suppose we want to cut the margin of error to 4%. What's the necessary sample size?
c) What sample size would produce a margin of error of 3%?