The article “Kids Digital Day: Almost 8 Hours” (USA Today, January 20, 2010) summarized results from a national survey of 2002 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group.
a. Of those surveyed, 1321 reported owning a cell phone. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone.
b. Of those surveyed, 1522 reported owning an MP3 music player. Use this information to construct and interpret a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player.
c. Explain why the confidence interval from Part (b) is narrower than the confidence interval from Part (a) even though the confidence level and the sample size used to compute the two intervals was the same.