In an article titled “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.
a. 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. Does this suggest that it is plausible to believe the proportion of 7- to 11-year-olds who rode their bike at least six times in 2004 is the same as in 1995?
b. Conduct a test of hypothesis to answer the question posed in part a. Are the results of parts a and b contradictory? Explain.