Question

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.

Answer 1

Answer: (0.293, 0.387)

Explanation:

Given : Sample size : n=387 ;

Number of ads use humor=130

The the sample proportion for television ads use humor :
`\hat{p}=(130)/(387)\approx0.34`

Significance level :
`\alpha:1-0.95=0.05`

Critical value =
`z_(\alpha/2)=\pm1.96`

The confidence interval for population proportion is given by :_

`\hat{p}\pm z_(\alpha/2)\sqrt{(p(1-p))/(n)}`

i.e.
`0.34\pm (1.96)\sqrt{(0.34(1-0.34))/(387)}`

`\approx0.34\pm 0.047=(0.34-0.047,0.34+0.047)\\\\=(0.293\ ,\ 0.387)`

Hence, the 95 percent confidence interval for the proportion of all U.K. television ads that use humor = (0.293, 0.387)