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.

According to a Food and Drug Administration (FDA) study, a cup of coffee contains an average of 115 milligrams (mg) of caffeine, with the amount per cup ranging from 60 to 180 mg. Suppose you want to repeat the FDA experiment in order to obtain an estimate of the mean caffeine content in a cup of coffee correct to within 5 mg with 95% confidence. How many cups of coffee would have to be included in your sample?

A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110. Test the null hypothesis that

$$\mu = 100$$

against the alternative hypothesis that

$$\mu > 100 , \text { using } \alpha = .05$$

Interpret the results of the test.

In each case, find the approximate sample size required to construct a 95% confidence interval for p that has sampling error SE = .06. a. Assume that p is near .3. b. Assume that you have no prior knowledge about p , but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

What is meant by the term "90% confident" when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately $90 \%$ of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately $90 \%$ of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately $90 \%$ of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population means in approximately $90 \%$ of the samples.

Hospital length of stay. Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS in the United States is $4.5$ days (Healthcare Cost and Utilization Project Statistical Brief, October 2014). A random sample of 20 hospitals in one state had a mean LOS of $3.8$ days and a standard deviation of $1.2$ days. Interpret the interval in terms of this application.

Largest private companies. IPOs-initial public offerings of stock-create billions of dollars of new wealth for owners, managers, and employees of companies that were previously privately owned. Nevertheless, hundreds of large and thousands of small companies remain privately owned. The revenues of a random sample of 15 firms from Forbes 216 Largest Private Companies list are given in the table below. What characteristic must the population possess to ensure the appropriateness of the estimation procedure used in part b?

Company	Revenue (in billions)
Toys, R, Us	$\$ 12.4$
Pilot Flying J	$31.0$
Tenaska Energy	$12.2$
Wawa	$9.7$
Gulf States Toyota	$8.0$
Brookshire Grocery	$2.5$
Sinclair Oil	$7.0$
Bose	$3.4$
Mary Kay	$4.0$
Drummond	$2.4$
Petco	$4.0$
SAS	$3.1$
Forever 21	$4.4$
Rock Ventures	$5.1$
Conair	$2.3$

The day after Thanksgiving - called Black Friday-is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of Retail and Distribution Management (Vol. 39, 2011). One question was "How many hours do you usually spend shopping on Black Friday?" Data for the 38 shoppers are listed in the accompanying table. Give a practical interpretation of the interval.

$$\begin{matrix} \text{6} & \text{6} & \text{4} & \text{4} & \text{3} & \text{16} & \text{4} & \text{4} & \text{5} & \text{6} & \text{6} & \text{5} & \text{5} & \text{4}\\ \text{6} & \text{5} & \text{6} & \text{4} & \text{5} & \text{4} & \text{4} & \text{4} & \text{7} & \text{12} & \text{5} & \text{8} & \text{6} & \text{10}\\ \text{5} & \text{8} & \text{8} & \text{3} & \text{3} & \text{8} & \text{5} & \text{6} & \text{10} & \text{11}\\ \end{matrix}$$

Henna Co. produces and sells two products, T and O. It manufactures these products in separate factories and markets them through different channels. They have no shared costs. This year, the company sold 50,000 units of each product. Sales and costs for each product follow. $$ \begin{matrix} & \text{Product T} & \text{Product O}\\ \text{Sales}\ldots\ldots\ldots & \text{\$2,000,000} & \text{\$2,000,000}\\ \text{Variable costs}\ldots\ldots\ldots & \text{1,600,000} & \text{250,000}\\ \text{Contribution margin}\ldots\ldots\ldots & \text{400,000} & \text{1,750,000}\\ \text{Fixed costs}\ldots\ldots\ldots & \text{125,000} & \text{1,475,000}\\ \text{Income before taxes }\ldots\ldots\ldots & \text{275,000} & \text{275,000}\\ \text{Income taxes (32\\% rate)}\ldots\ldots\ldots & \text{88,000} & \text{88,000}\\ \text{Net income} \ldots\ldots\ldots & \text{\$ 187,000} & \text{\$ 187,000}\\ \end{matrix} $$ 1. Compute the break-even point in dollar sales for each product. (Round the answer to whole dollars.) 2. Assume that the company expects sales of each product to decline to 30,000 units next year with no change in unit selling price. Prepare forecasted financial results for next year following the format of the contribution margin income statement as just shown with columns for each of the two products (assume a 32% tax rate). Also, assume that any loss before taxes yields a 32% tax benefit. 3. Assume that the company expects sales of each product to increase to 60,000 units next year with no change in unit selling price. Prepare forecasted financial results for next year following the format of the contribution margin income statement shown with columns for each of the two products (assume a 32% tax rate). 4. If sales greatly decrease, which product would experience a greater loss? Explain. 5. Describe some factors that might have created the different cost structures for these two products.

Use the casino game roulette. Roulette is played by spinning a wheel with 38 numbered slots. The numbers 1 through 36 appear on the wheel, half of them colored black and half colored red. Two slots, numbered 0 and 00, are colored green. A ball is placed on the spinning wheel and allowed to come to rest in one of the slots. Bets are placed on where the ball will land. You can bet that the ball will land on one of 0 or 00. If you win, the casino will pay you $17 for each dollar you bet. What is the probability of winning this bet?

According to recent studies, 1% of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post-laser vision problems ( All About Vision , 2006). In a random sample of 100,000 LASIK patients, let x be the number who experience serious post-laser vision problems. a. Find E ( x ). b. Find Var( x ). c. Find the z -score for x = 950. d. Find the approximate probability that fewer than 950 patients in a sample of 100,000 will experience serious post-laser vision problems.

Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Swedish civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns in the journal Giorisk (Vol. 7, 2013). The mixed soil was tested by advancing a cylindrical rod with a cone tip down into the soil. During penetration, the cone penetrometer measures the cone tip resistance (megapascals, MPa). The researchers established that tip resistance for the deep mixed soil followed a normal distribution with $\mu=2.2$ MPa and $\sigma=.9$ MPa. a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa. b. Find the probability that the tip resistance will exceed 1.0 MPa. c. Find a value of tip resistance, T, such that 35% of all soil samples have tip resistance values that exceed T.

A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A University of South Florida statistician hired by the company to investigate the level of contamination in the stored cartridges found that 23% of the cartridges in a particular lot were contaminated. Suppose you randomly sample (without replacement) gun cartridges from this lot until you find a contaminated one. Let x be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for x is given by the formula

$$p ( x ) = ( .23 ) ( .77 ) ^ { x - 1 } , x = 1,2,3 , \ldots$$

Find p(1) . Interpret this result.

Match each of the following definitions of costs to the cost classifications.

1. This cost increases in direct proportion to increases in volume: its amount is constant for each unit produced.

2. This cost remains constant over a limited range of volume; when it reaches the end of its limited range, it changes by a lump sum and remains at that level until it exceeds another limited range.

3. This cost has a component that remains the same over all volume levels and another component that increases in direct proportion to increases in volume.

4. This cost increases when volume increases, but the increase is not constant for each unit produced.

5. This cost remains constant over all volume levels within the productive capacity for the planning period.

6. This cost is the combined amount of all the other costs.

Choices:

a. Fixed cost

b. Mixed cost

c. Total cost

d. Curvilinear cost

e. Variable cost

f. Step-wise cost