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The formula used to calculate a large-sample confidence interval for \(p\) is $$ \hat{p} \pm(z \text { critical value }) \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$ What is the appropriate \(z\) critical value for each of the following confidence levels? a. \(90 \%\) b. \(99 \%\) c. \(80 \%\)

In a survey of 800 college students in the United States, 576 indicated that they believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action ("Listening to Dissenting Views Part of Civil Debate," USA TODAY, November 17,2015 ). Assuming that the sample is representative of college students in the United States, construct and interpret a \(95 \%\) confidence interval for the proportion of college students who have this belief.

Appropriate use of the interval $$ \hat{p} \pm(z \text { critical value }) \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$ requires a large sample. For each of the following combinations of \(n\) and \(\hat{p}\), indicate whether the sample size is large enough for this interval to be appropriate. a. \(n=100\) and \(\hat{p}=0.70\) b. \(n=40\) and \(\hat{p}=0.25\) c. \(n=60\) and \(\hat{p}=0.25\) d. \(n=80\) and \(\hat{p}=0.10\)

The USA Snapshot titled "Social Media Jeopardizing Your Job?" (USA TODAY, November 12,2014\()\) summarized data from a survey of 1855 recruiters and human resource professionals. The Snapshot indicted that \(53 \%\) of the people surveyed had reconsidered a job candidate based on his or her social media profile. Assume that the sample is representative of the population of recruiters and human resource professionals in the United States. a. Use the given information to estimate the proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile using a \(95 \%\) confidence interval. Give an interpretation of the interval in context and an interpretation of the confidence level of \(95 \%\). b. Would a \(90 \%\) confidence interval be wider or narrower than the \(95 \%\) confidence interval from Part (a)?

The article "Most Dog Owners Take More Pictures of Their Pet Than Their Spouse" (August \(22,2016,\) news .fastcompany.com/most-dog-owners-take-more- pictures-oftheir-pet-than-their-spouse-4017458, retrieved May 6,2017 ) indicates that in a sample of 1000 dog owners, 650 said that they take more pictures of their dog than their significant others or friends, and 460 said that they are more likely to complain to their dog than to a friend. Suppose that it is reasonable to consider this sample as representative of the population of dog owners. a. Construct and interpret a \(90 \%\) confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends. b. Construct and interpret a \(95 \%\) confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend. c. Give two reasons why the confidence interval in Part (b) is wider than the interval in Part (a).

The report "The 2016 Consumer Financial Literacy Survey" (The National Foundation for Credit Counseling, www.nfcc.org, retrieved October 28,2016 ) summarized data from a representative sample of 1668 adult Americans. Based on data from this sample, it was reported that over half of U.S. adults would give themselves a grade of \(\mathrm{A}\) or \(\mathrm{B}\) on their knowledge of personal finance. This statement was based on observing that 934 people in the sample would have given themselves a grade of \(\mathrm{A}\) or \(\mathrm{B}\). a. Construct and interpret a \(95 \%\) confidence interval for the proportion of all adult Americans who would give themselves a grade of \(\mathrm{A}\) or \(\mathrm{B}\) on their financial knowledge of personal finance. b. Is the confidence interval from Part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of \(\mathrm{A}\) or \(\mathrm{B}\) ? Explain why or why not.

The article "Should Canada Allow Direct-to-Consumer Advertising of Prescription Drugs?" (Canadian Family Physician [2009]: \(130-131\) ) calls for the legalization of advertising of prescription drugs in Canada. Suppose you wanted to conduct a survey to estimate the proportion of Canadians who would allow this type of advertising. How large a random sample would be required to estimate this proportion with a margin of error of \(0.02 ?\)

In spite of the potential safety hazards, some people would like to have an Internet connection in their car. A preliminary survey of adult Americans has estimated the proportion of adult Americans who would like Internet access in their car to be somewhere around 0.30 (USA TODAY, May 1 , 2009). Use the given preliminary estimate to determine the sample size required to estimate this proportion with a margin of error of 0.02

Data from a representative sample were used to estimate that \(32 \%\) of all computer users in 2011 had tried to get on a Wi-Fi network that was not their own in order to save money (USA TODAY, May 16,2011 ). You decide to conduct a survey to estimate this proportion for the current year. What is the required sample size if you want to estimate this proportion with a margin of error of \(0.05 ?\) Calculate the required sample size first using 0.32 as a preliminary estimate of \(p\) and then using the conservative value of \(0.5 .\) How do the two sample sizes compare? What sample size would you recommend for this study?

A random sample will be selected from the population of all adult residents of a particular city. The sample proportion \(\hat{p}\) will be used to estimate \(p,\) the proportion of all adult residents who are registered to vote. For which of the following situations will the estimate tend to be closest to the actual value of \(p ?\) I. \(\quad n=1000, p=0.5\) II. \(\quad n=200, p=0.6\) III. \(n=100, p=0.7\)