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.

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Phoebe Acevedo

18 December, 07:32

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.

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Hunter Fuller · Answer 1

confidence Interval = 0.448 - 0.492

Explanation:

Population, n = 2000

Confidence level = 0.9

Ratio of those that rode a bike at least 6 times, p = 0.47

Ratio of those that did not ride a bike for at least 6 times, q = 1 - p = 1-0.47 = 0.53

For 95% confidence level, z = 1.96

E = z * (pq/n) ^0.5

E = 1.96 * (0.53*0.47/2000) ^0.5

E = 0.022

The confidence interval is from (p-E) to (p+E)

p-E = 0.47 - 0.022 = 0.448

p+E = 0.47 + 0.022 = 0.492