A study by the Kaiser Family Foundation provided one of the first looks at media use among the very youngest children—those from 6 months to 6 years of age (Kaiser Family Foundation, 2003, www.kff.org). The director of the Kaiser Family Foundation’s Program for the Study of Entertainment Media and Health said, “It’s not just teenagers who are wired up and tuned in, its babies in diapers as well.” Because previous research indicated that children who have a TV in their bedroom spend less time reading than other children, the authors of the Foundation study were interested in learning about the proportion of kids who have a TV in their bedroom. They collected data from two independent random samples of parents. One sample consisted of parents of children ages 6 months to 3 years old. The second sample consisted of parents of children ages 3 to 6 years old. They found that the proportion of children who had a TV in their bedroom was 0.30 for the sample of children ages 6 months to 3 years and 0.43 for the sample of children ages 3 to 6 years old. Suppose that each of the two sample sizes was 100.
a. Construct and interpret a 95% large-sample confidence interval for the proportion of children ages 6 months to 3 years who have a TV in their bedroom.
b. Construct and interpret a 95% large-sample confidence interval for the proportion of children ages 3 to 6 years who have a TV in their bedroom.
c. Do the confidence intervals from Parts (a) and (b) overlap? What does this suggest about the two population proportions?
d. Construct and interpret a 95% large-sample confidence interval for the difference in the proportions for children ages 6 months to 3 years and for children ages 3 to 6 years.
e. Is the interval in Part (d) consistent with your answer in Part (c)? Explain.