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.

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.

Suppose x is a random variable for which a Poisson probability distribution with

$$\lambda = 3$$

provides a good characterization. a. Graph

$$p ( x ) \text { for } x = 0,1,2 , \ldots , 9$$

b. Find

$$\mu \text { and } \sigma$$

for x, and locate

$$\mu$$

and the interval

$$\mu \pm 2 \sigma$$

on the graph. c. What is the probability that x will fall within the interval

$$\mu \pm 2 \sigma ?$$

Tax returns audited by the IRS. According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 1 in 100 if your income is less than $\$ 1$ million and 9 in 100 if your income is $\$ 1$ million or more (IRS Enforcement and Services Statistics). If five taxpayers with incomes under $\$ 1$ million are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited?

Who prepares your tax return? As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers found that $37 \%$ of adult workers prepare their own tax return. Assume that this percentage applies to all U.S. adult workers. Now consider a random sample of 270 adult workers. Find the probability that more than 112 of the workers prepare their own tax return.

Examine the sample data in the accompanying table. Construct a steam-and-leave plot to access weather the data are from an approximately normal distribution.

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.

Salary of a travel management professional. According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is $\$ 94,000$. Assume that the standard deviation of such salaries is $\$ 30,000$. Consider a random sample of 50 travel management professionals and let $\bar{x}$ represent the mean salary for the sample. What is $\sigma_{\bar{x}}$ ?

Refer to Exercise and find $E(x)=\mu$. Then use the sampling distribution of $\bar{x}$ found in Exercise 5.3 to find the expected value of $\bar{x}$. Note that $E(\bar{x})=\mu$.

$$\begin{array}{llllll} \hline x & 1 & 2 & 3 & 4 & 5 \\ p(x) & .2 & .3 & .2 & .2 & .1 \\ \hline \end{array}$$

$$\begin{array}{cc|cc} \hline \text { Sample } & \text { Probability } & \text { Sample } & \text { Probability } \\ \hline 1,1 & .04 & 3,4 & .04 \\ 1,2 & .06 & 3,5 & .02 \\ 1,3 & .04 & 4,1 & .04 \\ 1,4 & .04 & 4,2 & .06 \\ 1,5 & .02 & 4,3 & .04 \\ 2,1 & .06 & 4,4 & .04 \\ 2,2 & .09 & 4,5 & .02 \\ 2,3 & .06 & 5,1 & .02 \\ 2,4 & .06 & 5,2 & .03 \\ 2,5 & .03 & 5,3 & .02 \\ 3,1 & .04 & 5,4 & .02 \\ 3,2 & .06 & 5,5 & .01 \\ 3,3 & .04 & & \\ \hline \end{array}$$