Norris Company implemented a quality improvement program and tracked the following for the 5 years:

$$\begin{array}{lccc} & \text { Quality Costs } & \text { Actual Sales } & \text { Costs as a Percentage of Sales } \\ \hline 20 \times 1 & \$ 880,000 & \$ 4,000,000 & 22.00 \% \\ 20 \times 2 & 840,000 & 4,200,000 & 20.00 \\ 20 \times 3 & 765,000 & 4,500,000 & 17.00 \\ 20 \times 4 & 700,000 & 5,000,000 & 14.00 \\ 20 \times 5 & 594,000 & 5,400,000 & 11.00 \end{array}$$

By cost category as a percentage of sales for the same period of time:

$$\begin{array}{lcccc} & \text { Prevention } & \text { Appraisal } & \text { Internal Failure } & \text { External Failure } \\ \hline 20 \mathrm{X} 1 & 1.50 \% & 2.50 \% & 6.50 \% & 11.50 \% \\ 20 \mathrm{X} 2 & 2.75 & 3.25 & 4.00 & 10.00 \\ 20 \mathrm{X} 3 & 3.00 & 5.00 & 2.75 & 6.25 \\ 20 \mathrm{X} 4 & 3.50 & 3.50 & 2.00 & 5.00 \\ 20 \mathrm{X} 5 & 3.75 & 2.25 & 1.50 & 3.50 \end{array}$$

1. Prepare a bar graph that reveals the trend in quality cost as a percentage of sales (time on the horizontal axis and percentages on the vertical). Comment on the message of the graph.

2. Prepare a bar graph for each cost category as a percentage of sales. What does this graph tell you?

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?

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. $1 \mathrm{kWh}=3.60 \times 10^6 \mathrm{~J}$.

A simple solar collector is built by placing a 5-cm-diameter clear plastic tube around a garden hose whose outer diameter is 1.6 cm. The hose is painted black to maximize solar absorption, and some plastic rings are used to keep the spacing between the hose and the clear plastic cover constant. During a clear day, the temperature of the hose is measured to be $65^\circ C,$ while the ambient air temperature is $26^\circ C.$ Determine the rate of heat loss from the water in the hose per meter of its length by natural convection. Also, discuss how the performance of this solar collector can be improved. Evaluate air properties at an average temperature of $50^\circ C$ and 1 atm pressure. Is this a good assumption?

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.

For the centrifugal water pump of the above problem, plot the pump's performance data: $H(\mathrm{~m})$, bhp (W), and $\eta_{\text {pump }}$ (percent) as functions of $\bar{V}(\mathrm{Lpm})$, using symbols only (no lines). Perform linear least-squares polynomial curve fits for all three parameters, and plot the fitted curves as lines (no symbols) on the same plot. For consistency, use a first-order curve fit for $H$ as a function of $\dot{V}^2$, use a second-order curve fit for bhp as a function of both $\vec{V}$ and $\dot{V}^2$, and use a third-order curve fit for $\eta_{p \text { pup }}$ as a function of $\dot{V}, \dot{V}^2$, and $V^3$. List all curve-fitted equations and coefficients (with units) for full credit. Find the BEP of the pump based on the curve-fitted expressions.

A spring-mass-damper system, as shown in Figure , is used as a shock absorber for a large high-performance motorcycle. The original parameters selected are $m=1 \mathrm{~kg}, b=9 \mathrm{~N} \mathrm{~s} / \mathrm{m}$, and $k=20 \mathrm{~N} / \mathrm{m}$. (a) Determine the system matrix, the characteristic roots, and the transition matrix $\boldsymbol{\Phi}(t)$. The harsh initial conditions are assumed to be $y(0)=1$ and $d y /\left.d t\right|_{t=0}=2$. (b) Plot the response of $y(t)$ and $y(t)$ for the first two seconds. (c) Redesign the shock absorber by changing the spring constant and the damping constant in order to reduce the effect of a high rate of acceleration force $\dot{y}(t)$ on the rider. The mass must remain constant at $1 \mathrm{~kg}$.

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.

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

Prof. Hardtack gave four Friday quizzes last semester in his senior tax accounting class. A random sample of 10 student scores is shown for each quiz.

(a) Find the sample mean, standard deviation, and coefficient of variation for each quiz.

(b) How do these data sets differ in terms of center and variability?

(c) Briefly describe and compare student performance on each quiz.

Quiz 1: 60, 60, 60, 60, 71, 73, 74, 75, 88, 99

Quiz 2: 65, 65, 65, 65, 70, 74, 79, 79, 79, 79

Quiz 3: 66, 67, 70, 71, 72, 72, 74, 74, 95, 99

Quiz 4: 10, 49, 70, 80, 85, 88, 90, 93, 97, 98

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 inventory/stock turnover 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.

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

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

A two-stage compression refrigeration system operates with refrigerant-134a between the pressure limits of 1.4 and 0.10 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The refrigerant leaving the low-pressure compressor at 0.4 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 0.25 kg/s through the condenser, and (c) the coefficient of performance.

The following table shows the ranks given by two judges to the performance of six finalists in a men's figure skating competition:|

$$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Skater } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \text { Judge 1 } & 6 & 5 & 4 & 3 & 2 & 1 \\ \hline \text { Judge 2 } & 5 & 6 & 4 & 3 & 1 & 2 \\ \hline \end{array}$$

a. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is different from zero.

b. Calculate and interpret the Spearman rank correlation coefficient $r_s$.

c. The $p$-value for the test is found to be equal to $0.033$. At the $5 \%$ significance level, does the Spearman rank correlation coefficient differ from zero? Explain.

You are concerned about the effects of texting on driving performance. Design a study to test the response time of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes? a. Describe the explanatory and response variables in the study. b. What are the treatments? c. What should you consider when selecting participants? d. Your research partner wants to divide participants randomly into two groups: one to drive without distraction and one to text and drive simultaneously. Is this a good idea? Why or why not? e. Identify any lurking variables that could interfere with this study. f. How can blinding be used in this study?