1. A pollster took a random sample of 100 students from a large university and computed a 95% confidence interval to estimate the percentage of students who were planning to vote in the upcoming election. After examining the results, the pollster felt that the confidence interval was too wide to provide a precise estimate of p, the true percentage. What could the pollster have done to produce a narrower confidence interval that would produce a more precise estimate of the percent of all university students who plan to vote in the upcoming election?

2. Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test where H₀: the food is safe, and H₁: the food is not safe. The inspector says the food is safe, but it is actually not safe. What type of error does the inspector make?

3. It is reported that scores on a particular test of historical trivia given to high school students are approximately normally distributed with a mean of 85. Mrs. Rose believes that her high school seniors will score significantly better than the national average on this test based on the instruction they receive in her American History course. At the end of the semester, Mrs. Rose administers the historical trivia test to her students. The students score an average of 89 on this test, with a standard deviation of 2. After conducting the appropriate statistical test, Mrs. Rose finds that the p-value is .0025. Unfortunately, Mrs. Rose knows little about statistics and cannot understand what this p-value is telling her. Interpret the p-value for Mrs. Rose.