In an article entitled "Childhood Pastimes Are Increasingly Moving Indoors," Dennis Cauchon asserts that there have been huge declines in spontaneous outdoor activities such as bike riding, swimming, and touch football. In the article, he cites separate studies by the national Sporting Goods Association and American Sports Data that indicate bike riding alone is down 31% from 1995 to 2004. According to the surveys, 68% of 7- to 11-year-olds rode a bike at least six times in 1995 and only 47% did in 2004. Assume the sample sizes were 1,500 and 2,000, respectively. Calculate a 95% confidence interval to estimate the proportion of 7- to 11-year-olds who rode their bike at least six times in 2004.
A) (0.4481, 0.4919)
B) (0.4324, 0.4676)
C) (0.4021, 0.5179)
D) (0.4712, 0.4888).

Question

Quizplus · Accepted Answer

The correct answer is A because the 95% confidence interval for the proportion of 7- to 11-year-olds who rode their bike at least six times in 2004 is (0.4481, 0.4919). This interval was calculated using the formula for the confidence interval for a proportion, which is:sample proportion +/- z * sqrt((sample proportion * (1 - sample proportion)) / sample size)where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z = 1.96. Plugging in the values from the question, we get:0.47 +/- 1.96 * sqrt((0.47 * (1 - 0.47)) / 2000) = (0.4481, 0.4919)

In an Article Entitled "Childhood Pastimes Are Increasingly Moving Indoors