Constructing and Interpreting Confidence Intervals. In Exercises 13–16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.


Tennis Challenges In a recent U.S. Open tennis tournament, men playing singles matches used challenges on 240 calls made by the line judges. Among those challenges, 88 were found to be successful with the call overturned. Construct a 95% confidence interval for the proportion of successful challenges.

You wish to estimate with $90\%$ confidence the population proportion of people in Gen-Z that use social media. If you want your estimate to be accurate within $4\%$ of the population proportion, what is the minimum sample size needed? 

Your company has asked you to estimate the proportion of people who prefer the color red over other primary colors for manufacturing purposes. If they want the estimate to be within $.01$ of the true proportion with $95\%$ confidence, how many people should you survey?  

You want to make a $97\%$ confidence interval for the population proportion of people between $20-30$ years old who have gotten a speeding ticket in the past $2$ years. A prior study found that $26\%$ of people between $20-30$ years old have received a speeding ticket in the last year. If you want your estimate to be accurate within $3\%$ of the true population proportion, what is the minimum sample size needed? 

Arm Circumferences Arm circumferences of adult men are normally distributed with a mean of 33.64 cm and a standard deviation of 4.14 cm (based on Data Set 1 “Body Data” in Appendix B). A sample of 25 men is randomly selected and the mean of the arm circumferences is obtained.

b. What is the mean of all such sample means?

Formats of Confidence Intervals. In Exercises 9–12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 38 “Candies” in Appendix B.)

Green M&Ms Express 0.116 < p < 0.192 in the form of p +-E.

"Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Internet Use A random sample of 5005 adults in the United States includes 751 who do not use the Internet (based on three Pew Research Center polls). Construct a 95% confidence interval estimate of the percentage of U.S. adults who do not use the Internet. Based on the result, does it appear that the percentage of U.S. adults who do not use the Internet is different from 48%, which was the percentage in the year 2000?"

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.

b. Based on the result from part (a), is it safe to say that the majority of the population does not feel that the song is too offensive.

Confidence Levels

Given specific sample data, such as the data given in Exercise 1, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?