Question

Fewer young people are driving. In 1983, 87 percent of 19 year-olds had a driver's license. Twenty-five years later that percentage had dropped to 75 percent (University of Michigan Transportation Research Institute website, April 7, 2012). Suppose these results are based on a random sample of 1200 nineteen year-olds in 1983 and again in 2008.a. At 95% confidence, what is the margin of error and the interval estimate of the number of nineteen year old drivers in 1983? Round your answers to three decimal places.Margin of error = (four decimal places)Interval estimate = tob. At 95% confidence, what tis the margin of error and the interval estimate of the number of nineteen year old drivers in 2008? Round your answers to four decimal places.Margin of error =Interval estimate = toc. Is the margin of error the same in parts (a) and (b)?- Select your answer -YesWhy, or why not?

Answer 1

The question doesn't ask you to find the standard deviation, but rather the margin of error. The answer is NO, they are NOT THE SAME because one equals 1 and the other equals 0.0025.

Explanation:

In a confidence interval, the margin of error is everything to the right of the +/-, which is the critical value standard error. Since you're dealing with proportions, in this case the critical value is Z_.05=1.65. The standard error of a proportion is sqrt(pi_hat(1-pi_hat)/n). So to get the margin of error you calculate 1.65sqrt(pi_hat(1-pi_hat)/n).