1. A poll of 72 seniors, taken three weeks before the selection of the school Homecoming Queen, identified 60 who planned to vote for Jenny Wonderful. Unfortunately, a week after the poll was taken, the school newspaper ran an article that quoted Jenny slandering her opponents. Another poll of 80 seniors taken shortly after the article appeared showed that 56 planned to vote for Jenny. Does this indicate a significant drop in support for Jenny? Use good statistical reasoning to support your answer. (25 points)

2. You're interested in the proportion of students in your school who favor the elimination of a local curfew on teenagers. Assume your school has 1,000 students.

A. To generate a 95% confidence interval for the proportion of students who favor the elimination of a curfew, what's the minimum number of students you need if you want the margin of error to be 5%? (9 points)

B. Suppose your principal, who never took a statistics class, says that a 5% margin of error just isn't accurate enough. He wants you to produce a confidence interval with a margin of error of only 2.5%. How big does your sample have to be now? What do you think of the principal's proposal?

(9 points)

C. In general, if you wanted to cut the margin of error for a given confidence level in half, by what amount would you have to increase the sample size?

Use the formula for minimum sample size to explain your answer. (9 points)