The article “Portable MP3 Player Ownership Reaches New High” (Ipsos Insight, June 29, 2006) reported that in 2006, 20% of those in a random sample of 1,112 Americans ages 12 and older indicated that they owned an MP3 player. In a similar survey conducted in 2005, only 15% reported owning an MP3 player. Suppose that the 2005 figure was also based on a random sample of size 1,112.
a. Are the sample sizes large enough to use the large-sample confidence interval for a difference in population proportions?
b. Estimate the difference in the proportion of Americans ages 12 and older who owned an MP3 player in 2006 and the corresponding proportion for 2005 using a 95% confidence interval.
c. Is zero included in the confidence interval? What does this suggest about the change in this proportion from 2005 to 2006?
d. Interpret the confidence interval in the context of this problem.