Eye shadow, mascara, and nickel allergies. Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye shadow or mascara? This was the question of interest in a paper published in the Journal of the European Academy of Dermatology and Venereology (June 2010). In a sample of 131 women with cosmetic dermatitis from using eye shadow, 12 were diagnosed with a nickel allergy. In a sample of 250 women with cosmetic dermatitis from using mascara, 25 were diagnosed with a nickel allergy. Compute a $95 \%$ confidence interval for the proportion of women with cosmetic dermatitis from using mascara who have a nickel allergy. Interpret the result.

Are you really being served red snapper? Refer to the Nature (July 15, 2004) study of fish specimens labeled "red snapper," Exercise 3.75 (p. 172). Recall that federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. A team of University of North Carolina (UNC) researchers analyzed the meat from each in a sample of 22 "red snapper" fish fillets purchased from vendors across the United States in an effort to estimate the true proportion of fillets that are really red snapper. DNA tests revealed that 17 of the 22 fillets (or $77 \%$ ) were not red snapper but the cheaper, look-alike variety of fish.

Explain why a large-sample confidence interval is inappropriate to apply in this study.

Are you really being served red snapper? Refer to the Nature (July 15, 2004) study of fish specimens labeled "red snapper," . Recall that federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane snapper) to customers who order red snapper. A team of University of North Carolina (UNC) researchers analyzed the meat from each in a sample of 22 "red snapper" fish fillets purchased from vendors across the United States in an effort to estimate the true proportion of fillets that are really red snapper. DNA tests revealed that 17 of the 22 fillets (or $77 \%$ ) were not red snapper but the cheaper, look-alike variety of fish.

Identify the parameter of interest to the UNC researchers.

Diamonds sold on the open market. Refer to the sample of 308 diamond stones that were listed for sale on the open market in Singapore's Business Times. Recall that the color of each diamond is classified as D, E, F, G, H, or I, while the clarity of each is classified as VVS1, VVS2, VS1, or VS2. Find a $99 \%$ confidence interval for the proportion of all diamonds for sale on the open market that are classified as "VS1" clarity. Interpret the result.

Diamonds sold on the open market. Refer to the sample of 308 diamond stones that were listed for sale on the open market in Singapore's Business Times. Recall that the color of each diamond is classified as D, E, F, G, H, or I, while the clarity of each is classified as VVS1, VVS2, VS1, or VS2. Find a $99 \%$ confidence interval for the proportion of all diamonds for sale on the open market that are classified as "D" color. Interpret the result.

The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10, 2009), researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. Use Wilson’s adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result.

The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. In High Altitude Medicine & Biology (Vol. 10, 2009), researchers provided official recommendations for mountain emergency medicine. As part of the document, the researchers examined the likelihood of needing certain types of splints. A Scottish Mountain Rescue study reported that there was 1 femoral shaft splint needed among 333 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. Is the sample large enough to apply the large-sample estimation method of this section? Show why or why not.

As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The international Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano international Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comn1ent on the accuracy of this estimate. Use a 95% confidence interval to support your inference.

Minority ownership of franchises. According to a 2011 report for IFA Educational Foundation, $20.5 \%$ of all franchised businesses in the United States are minority owned. (This information is based on the U.S. Census Bureau's survey of 27 million business owners.) Suppose that you obtain a sample of 100 franchised businesses located in Mississippi and find that 15 are owned by minorities. Does this result lead you to conclude that the percentage of minority-owned franchises in Mississippi is less than the national value of $20.5 \%$ ? Explain.

Who prepares your tax return? Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise $5.50$ (p. 297). Recall that in a sample of 270 U.S. adult workers, the researchers found that $37 \%$ prepare their own tax return. According to the researchers, about $70 \%$ of the sampled workers were recruited from a shopping mall (where they were reimbursed $\$ 5$ for their time) and about $30 \%$ were full-time workers enrolled in a professional graduate degree program. How might this information impact the inference you made in part $\mathbf{b}$ ?

Who prepares your tax return? Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise $5.50$ (p. 297). Recall that in a sample of 270 U.S. adult workers, the researchers found that $37 \%$ prepare their own tax return. Suppose an IRS tax consultant claims that $50 \%$ of all U.S. adult workers prepare their own tax return. Make an inference about this claim.

Who prepares your tax return? Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise $5.50$ (p. 297). Recall that in a sample of 270 U.S. adult workers, the researchers found that $37 \%$ prepare their own tax return. Construct a $99 \%$ confidence interval for the true proportion of all U.S. adult workers who prepare their own tax return.

Cybersecurity survey. Refer to the State of Cybersecurity (2015) survey of firms from around the world, Exercise $1.20$ (p. 26). Recall that of the 766 firms that responded to the survey, 628 (or $82 \%$ ) expect to experience a cyberattack (e.g., a Malware, hacking, or phishing attack) during the year. Estimate the probability of an expected cyberattack at a firm during the year with a $90 \%$ confidence interval. Explain how $90 \%$ is used as a measure of reliability for the interval.

Nannies who are INA certified. The International Nanny Association (INA) reports that in a sample of 928 inhome child care providers (nannies), 128 have passed the INA Nanny Credential Exam (2014 International Nanny Association Salary and Benefits Survey). Use Wilson's adjustment to find a $95 \%$ confidence interval for the true proportion of all nannies who have passed the INA certification exam.