Refrigeration units can be rated in "tons." A 1-ton air conditioning system can remove sufficient energy to freeze 1 British ton $\left(2000\right.$ pounds $=909 \mathrm{~kg}$ ) of $0^{\circ} \mathrm{C}$ water into $0^{\circ} \mathrm{C}$ ice in one 24-h day. If, on a $35^{\circ} \mathrm{C}$ day, the interior of a house is maintained at $22^{\circ} \mathrm{C}$ by the continuous operation of a 5 -ton air conditioning system, how much does this cooling cost the homeowner per hour? Assume the work done by the refrigeration unit is powered by electricity that costs $\$ 0.10$ per $\mathrm{kWh}$ and that the unit's coefficient of performance is $15 \%$ that of an ideal refrigerator. $1 \mathrm{kWh}=3.60 \times 10^6 \mathrm{~J}$.

Performance of stock screeners. Recall, from Exercise $6.36$ (p. 326), that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated in the accompanying table. You want to determine whether $\mu$, the average annualized return for all AAII stock screeners, is positive (which implies that the stock screeners perform better, on average, than the S&P 500). An XLSTAT printout of the analysis is shown on the top of page 394. Locate the observed significance level ( $p$-value) on the printout.

You are evaluating the performance of a large electromagnet. The magnetic field of the electromagnet is zero at $t=0$ and increases as the current through the windings of the electromagnet is increased. You determine the magnetic field as a function of time by measuring the time dependence of the current induced in a small coil that you insert between the poles of the electromagnet, with the plane of the coil parallel to the pole faces as in Fig. we saw earlier. The coil has 4 turns, a radius of $0.800 \mathrm{~cm}$, and a resistance of $0.250 \Omega$. You measure the current $i$ in the coil as a function of time 1 . Your results are shown in FLFig. we saw earlier. Throughout your measurements, the current induced in the coil remains in the same direction. Calculate the magnetic field at the location of the coil for $t=2.00 \mathrm{~s}$,

Performance data for a pump are

$$\begin{matrix} \text{H (ft)} & \text{90} & \text{87} & \text{81} & \text{70} & \text{59} & \text{43} & \text{22}\\ \text{Q (cfm)} & \text{0} & \text{50} & \text{100} & \text{150} & \text{200} & \text{250} & \text{300}\\ \end{matrix}$$

The pump is to be used to move water between two open reservoirs with an elevation increase of 24 ft. The connecting pipe system consists of 1750 ft of commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve. Find the flow rate if we use (a) 8-in., (b) 10-in., and (c) 12-in. (nominal) pipe.

Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a 10-game period, the scores of these two players are shown in the accompanying table. Assume that the two samples are drawn independently from normally distributed populations.

$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Player 1 } & 13 & 15 & 12 & 18 & 14 & 15 & 11 & 13 & 11 & 16 \\ \hline \text { Player 2 } & 11 & 21 & 18 & 9 & 20 & 11 & 13 & 11 & 19 & 8 \\ \hline \end{array}$$

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Evaluate a strategy Total Oil might use to improve its efficiency and gearing.

Performance of stock screeners. Investment companies provide their clients with automated tools-called stock screeners to help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Web site, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor's 500 Index) for 13 randomly selected stock screeners. (Note: A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.) Compute the median for the data set. Interpret its value.

$$\begin{array}{lllllllllllll}9.0 & -.1 & -1.6 & 14.6 & 16.0 & 7.7 & 19.9 & 9.8 & 3.2 & 24.8 & 17.6 & 10.7 & 9.1\end{array}$$

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Calculate the debtor days ratio for Total Oil in $2013$.

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Evaluate Total Oil's efficiency and gearing.

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions (“Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds,” NHTSA, DOT HS 811 488, June 2011):

$$\begin{matrix} \text{32.1} & \text{30.6} & \text{31.4} & \text{30.4} & \text{31.0} & \text{31.9}\\ \end{matrix}$$

The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using $\alpha=.01$.

Performance data for a pump are

$$\begin{matrix}\text{H (ft)} & \text{179} & \text{176} & \text{165} & \text{145}\\\text{Q (gpm)} & \text{0} & \text{500} & \text{1000} & \text{1500}\\\text{H (ft)} & \text{119} & \text{84} & \text{43}\\\text{Q (gpm)} & \text{2000} & \text{2500} & \text{3000}\\\end{matrix}$$

Estimate the delivery when the pump is used to move water between two open reservoirs through 1200 ft of 12-in.-diameter commercial steel pipe containing two $90^{\circ}$ elbows and an open gate valve if the elevation increase is 50 ft. Determine the gate valve loss coefficient needed to reduce the volume flow rate by half.

Various techniques have been proposed to curb cross-border drug smuggling into a country. The costs of implementing each strategy along a particularly rugged section of the border are indicated below. The table also includes a score that is compiled based on deterrence, interdiction, and apprehension, with a higher score indicating better performance. For a budget of $60 million, determine which techniques should be employed on the basis of a cost-effectiveness analysis.$

$$\begin{array}{lcc} \text { Activity } & \text { cost, } \$ \text { Millions } & \text { Score } \\ \hline \text { Tethered aerostats } & 3.8 & 8 \\ \text { Boots-on-the-ground } & 31.4 & 52 \\ \text { Fence } & 18.7 & 12 \\ \text { Motion sensors } & 9.8 & 7 \\ \text { Seismic sensors } & 8.3 & 5 \\ \text { Drones } & 12.1 & 26 \\ \hline \end{array}$$

$

SAT Performance. The Scholastic Aptitude Test (SAT) contains three parts: critical reading, mathematics, and writing. Each part is scored on an 800 -point scale. Information on test scores for the 2009 version of the SAT is available at the College Board website. A sample of SAT scores for six students follows.

$$\begin{array}{cccc} \text { Student } & \begin{array}{c} \text { Critical } \\ \text { Reading } \end{array} & \text { Mathematics } & \text { Writing } \\ 1 & 526 & 534 & 530 \\ 2 & 594 & 590 & 586 \\ 3 & 465 & 464 & 445 \\ 4 & 561 & 566 & 553 \\ 5 & 436 & 478 & 430 \\ 6 & 430 & 458 & 420 \end{array}$$

Using a .05 level of significance, do students perform differently on the three portions of the SAT?

Oil executives frequently compare the performance and efficiency of their company with those of other major oil companies. The following data is taken from Total Oil's $2013$ accounts.

$$\begin{array}{|l|l|l|l|l|l|l|l|} \hline\text{ Credit } & \text{ Creditors } & \text{ Debtors } & \text{ Long-term } & \text{ Inventories } & \text{ Cost of } & \text{ Capital } & \text{ Credit }\\ \text{ sales (\$m)} & \text{ (accounts } & \text{ (accounts } & \text{ loans(\$m)} & \text{ (\$m) } & \text{ sales (\$m) } & \text{ employed } & \text{ purchases } \\ & \text{ payable) } & \text{ receivable) } &&&& \text{ (\$m) } & \text{ (author’s } \\ & \text{ (\$m) } & \text{ (\$m) } &&&&& \text{ estimate)(\$m)} \\ \hline227969 & 30282 & 23422 & 34574 & 22097 & 160849 & 177555 & 160000 \\ \hline \end{array}$$

Calculate the creditor days ratio for Total Oil in $2013$.