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28 October, 14:58

41.

Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver's license.

Twenty-five years later that percentage had dropped to 75% (University of Michigan

Transportation Research Institute website, April 7, 2012). Suppose these results are based

on a random sample of 1200 19-year-olds in 1983 and again in 2008.

a. At 95% confidence, what is the margin of error and the interval estimate of the num-

ber of 19-year-old drivers in 1983?

b. At 95% confidence, what is the margin of error and the interval estimate of the num-

ber of 19-year-old drivers in 2008?

C. Is the margin of error the same in parts (a) and (b) ? Why or why not?

+5
Answers (1)
  1. 28 October, 17:39
    0
    a) (0.8509718, 0.8890282)

    b) (0.7255, 0.7745)

    Explanation:

    (a)

    Given that, a = 0.05, Z (0.025) = 1.96 (from standard normal table)

    So Margin of error = Z * sqrt (p * (1-p) / n) = 1.96 * sqrt (0.87 * (1-0.87) / 1200)

    =0.01902816

    So 95 % confidence interval is

    p+/-E

    0.87+/-0.01902816

    (0.8509718, 0.8890282)

    (b)

    Margin of error = 1.96 * sqrt (0.75 * (1-0.75) / 1200) = 0.0245

    So 95% confidence interval is

    p+/-E

    0.75+/-0.0245

    (0.7255, 0.7745)
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