Controversial Song The song “Baby It’s Cold Outside” generated...

Question

Controversial Song The song “Baby It’s Cold Outside” generated much controversy because of its lyrics and tone. CBS New York conducted a survey by asking viewers to use the Internet to respond to a question asking whether that song was really too offensive to play. Among 1043 Internet users who chose to respond, 986 said that the song was not too offensive, and 57 of the respondents said that the song was too offensive.

a. Construct a 95% confidence interval estimate of the proportion of the population having the belief that the song is not too offensive.

a. Construct a 95% confidence interval estimate of the proportion of the population having the belief that the song is not too offensive.

Accepted Answer

All right, hello, everyone. So this question says, a news website asks visitors to vote online on whether a newly released public service advertisement is respectful or disrespectful. Of the 1500 visitors who responded, 1230 said the ad was respectful, and 270 said it was disrespectful. Construct a 95% confidence interval estimate of the true proportion of all viewers who believe the ad is respectful. All right, so first, let's begin with the point estimate or PHAT. In this case, it's the proportion of people in this specific sample that reported the ad to be respectful. So in this case, that would be 1230 divided by 1500, which equals 0.82. From here So from here you would look for the critical value for the 95% confidence interval. In this case, the Z value, that's the critical value, would equal approximately 1.96. After you've obtained this information, you can now calculate the standard error, or SE. Now SE if you recall. Is equal to Phat multiplied by one subtracted by Phat. Divided by N, which is the sample size. So plugging in the given information SE. Is equal to 0.82 Multiplied by 1 subtracted by 0.82. Divided by the sample size of 1500. So evaluating this expression gives you a standard error of approximately 0.009920. And now you can calculate the margin of error and proceed with calculating the confidence interval itself. So, In this case, the margin of error, that's capital E is equal to the critical Z value that was obtained earlier, multiplied by the standard error. So here, that would be 1.96 multiplied by. 0.009920. And that gives you approximately 0.019443. So at this point, to find the confidence interval, that is to find both the lower and upper bounds of the confidence interval, you would take Phat. And add and subtract. The margin of error. So that would be 0.82 added to and then subtracted by 0. 019443 To once again find both limits of the confidence interval. And so when you do this, you find that the lower bound is 0.8006. And the upper bound is 0.8394. Now Converting this into percentages, we would multiply both numbers by 100, so the final answer for the confidence interval. Is Between 80.06%. And 83.94%. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

Key Concepts

Confidence Interval

Proportion

Sample Size and Its Impact

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