Q:

In an article in the Journal of Advertising, Weinberger and Spotts compare the use of humor in television ads in the United States and the United Kingdom. They found that a substantially greater percentage of U.K. ads use humor. (a) Suppose that a random sample of 387 television ads in the United Kingdom reveals that 130 of these ads use humor. Find a point estimate of and a 95 percent confidence interval for the proportion of all U.K. television ads that use humor.

Accepted Solution

A:
Answer: (0.293, 0.387)Step-by-step explanation:Given : Sample size : n=387  ;Number of ads use humor=130The the sample proportion for television ads use humor : [tex]\hat{p}=\dfrac{130}{387}\approx0.34[/tex]Significance level : [tex]\alpha:1-0.95=0.05[/tex]Critical value = [tex]z_{\alpha/2}=\pm1.96[/tex]The confidence interval for population proportion is given by :_ [tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]i.e.  [tex]0.34\pm (1.96)\sqrt{\dfrac{0.34(1-0.34)}{387}}[/tex][tex]\approx0.34\pm 0.047=(0.34-0.047,0.34+0.047)\\\\=(0.293\ ,\ 0.387)[/tex]Hence, the 95 percent confidence interval for the proportion of all U.K. television ads that use humor = (0.293, 0.387)