Chapter 8.3, Problem 26E

The article referenced in the previous exercise reported that for people age 18 to 29 who prefer to watch the news, the proportion who prefer to watch online is 0.37. Answer the questions posed in Parts (a)–(d) of the previous exercise for the population of people age 18 to 29 who prefer to watch the news.

The article “Younger Adults More Likely than Their Elders to Prefer Reading the News” (October 6, 2016, pewresearch.org/fact-tank/2016/10/06/younger-adults-more-likely-than-their-elders-to-prefer-reading-news/, retrieved March 28, 2018) estimated that only 3% of those age 65 and older who prefer to watch the news, rather than to read or listen to news, watch the news online. This estimate was based on a large sample of adult Americans conducted by the Pew Research Center. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news and suppose that for this population the actual proportion who prefer to watch online is 0.03. (Hint: See Example 8.9.)

1. a. A random sample of n = 100 people will be selected from this population and $\hat{p}$, the proportion of people who prefer to watch online will be calculated. What are the mean and standard deviation of the sampling distribution of $\hat{p}$?
2. b. Is it reasonable to assume that the sampling distribution of $\hat{p}$ is approximately normal for random samples of size n = 100? Explain.