Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

c. Develop the least squares estimated regression equation.

Broker Satisfaction. The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members on their experiences with discount brokers. As part of the survey, members were asked to rate the quality of the speed of execution with their broker as well as provide an overall satisfaction rating for electronic trades. Possible responses (scores) were no opinion $(0)$, unsatisfied (1), somewhat satisfied (2), satisfied (3), and very satisfied (4). For each broker summary scores were computed by calculating a weighted average of the scores provided by each respondent. A portion of the survey results follow (AAII website, February 7, 2012).

$$\begin{array}{lcc}\text { Brokerage } & \text { Speed } & \text { Satisfaction } \\ \text { Scottrade, Inc. } & 3.4 & 3.5 \\ \text { Charles Schwab } & 3.3 & 3.4 \\ \text { Fidelity Brokerage Services } & 3.4 & 3.9 \\ \text { TD Ameritrade } & 3.6 & 3.7 \\ \text { E*Trade Financial } & 3.2 & 2.9 \\ \text { Vanguard Brokerage Services } & 3.8 & 2.8 \\ \text { USAA Brokerage Services } & 3.8 & 3.6 \\ \text { Thinkorswim } & 2.6 & 2.6 \\ \text { Wells Fargo Investments } & 2.7 & 2.3 \\ \text { Interactive Brokers } & 4.0 & 4.0 \\ \text { Zecco.com } & 2.5 & 2.5\end{array}$$

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

Develop an estimated regression equation using trade price and speed of execution to predict overall satisfaction with the broker.

Federal Employee Satisfaction. The United States Office of Personnel Management (OPM) manages the civil service of the federal government. Results from its annual Federal Employee Viewpoint Survey (FEVS) are used to measure employee satisfaction on several work aspects, including Job Satisfaction, Pay Satisfaction, Organization Satisfaction, and an overall measure of satisfaction referred to as Global Satisfaction. In each case a 100-point scale with higher values indicating greater satisfaction is used (OPM website). Scores for Global Satisfaction. Job Satisfaction, Pay Satisfaction, and Organization Satisfaction for a sample of 65 employees are provided in the file Satisfaction.

b. Predict the overall Global Satisfaction score for an employee with a Job Satisfaction score of 72, a Pay Satisfaction score of 54, and an Organization Satisfaction score of 53.

Helen Bowers, owner of Helen’s Fashion Designs, is planning to request a line of credit from her bank. She has estimated the following sales forecasts for the firm for parts of 2016 and 2017.

$$\begin{matrix} \text{May 2016} & \text{\$ 180.000}\\ \text{June} & \text{180.000}\\ \text{July} & \text{360.000}\\ \text{August} & \text{540.000}\\ \text{September} & \text{720.000}\\ \text{October} & \text{360.000}\\ \text{November} & \text{360.000}\\ \text{December} & \text{90.000}\\ \text{January 2017} & \text{180.000}\\ \end{matrix}$$

Estimates regarding payments obtained from the credit department are as follows: collected within the month of sale, 10%; collected the month following the sale, 75%; collected the second month following the sale, 15%. Payments for labor and raw materials are made the month after these services were provided. Here are the estimated costs of labor plus raw materials:

$$\begin{matrix} \text{May 2016} & \text{\$ 90.000}\\ \text{June} & \text{90.000}\\ \text{July} & \text{126.000}\\ \text{August} & \text{882.000}\\ \text{September} & \text{306.000}\\ \text{October} & \text{234.000}\\ \text{November} & \text{162.000}\\ \text{December} & \text{90.000}\\ \end{matrix}$$

General and administrative salaries are approximately $27,000 a month. Lease payments under long-term leases are$9,000 a month. Depreciation charges are $36,000 a month. Miscellaneous expenses are$2,700 a month. Income tax payments of $63,000 are due in September and December. A progress payment of$180,000 on a new design studio must be paid in October. Cash on hand on July 1 will be $132,000, and a minimum cash balance of$90,000 should be maintained throughout the cash budget period. a. Prepare a monthly cash budget for the last 6 months of 2016. b. Prepare monthly estimates of the required financing or excess funds—that is, the amount of money Bowers will need to borrow or will have available to invest. c. Now suppose receipts from sales come in uniformly during the month (that is, cash receipts come in at the rate of 1/30 each day), but all outflows must be paid on the 5th. Will this affect the cash budget? That is, will the cash budget you prepared be valid under these assumptions? If not, what could be done to make a valid estimate of the peak financing requirements? No calculations are required, although if you prefer, you can use calculations to illustrate the effects. d. Bowers’ sales are seasonal; and her company produces on a seasonal basis, just ahead of sales. Without making any calculations, discuss how the company’s current and debt ratios would vary during the year if all financial requirements were met with short-term bank loans. Could changes in these ratios affect the firm’s ability to obtain bank credit? Explain.

Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

a. Develop a scatter diagram for these data with the room rate as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $\$128$, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

Broker Satisfaction Conclusion. In exercise 8, ratings data on $x=$ the quality of the speed of execution and $y=$ overall satisfaction with electronic trades provided the estimated regression equation $\hat{y}=.2046+.9077 x$ (AAII website). At the $.05$ level of significance, test whether speed of execution and overall satisfaction are related. Show the ANOVA table. What is your conclusion?

The American Association of Individual Investors publishes an annual guide to the top mutual funds (The Individual Investor’s Guide to the Top Mutual Funds, 22e, American Association of Individual Investors, 2003). The total risk ratings for 29 categories of mutual funds are as follows.

$$\begin{matrix} \text{ } & \text{Number of Fund}\\ \text{Total Risk} & \text{Categories}\\ \text{Low} & \text{7}\\ \text{Below Average} & \text{6}\\ \text{Average} & \text{3}\\ \text{Above Average} & \text{6}\\ \text{High} & \text{7}\\ \end{matrix}$$

What are the expected value and variance for total risk?

Passing and Winning in the NFL. The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season (NFL website).

$$\begin{array}{lcc}\text { Team } & \text { Yds/Att } & \text { WinPct } \\ \text { Arizona Cardinals } & 6.5 & 50 \\ \text { Atlanta Falcons } & 7.1 & 63 \\ \text { Carolina Panthers } & 7.4 & 38 \\ \text { Chicago Bears } & 6.4 & 50 \\ \text { Dallas Cowboys } & 7.4 & 50 \\ \text { New England Patriots } & 8.3 & 81 \\ \text { Philadelphia Eagles } & 7.4 & 50 \\ \text { Seattle Seahawks } & 6.1 & 44 \\ \text { St. Louis Rams } & 5.2 & 13 \\ \text { Tampa Bay Buccaneers } & 6.2 & 25\end{array}$$

d. Provide an interpretation for the slope of the estimated regression equation.

Passing and Winning in the NFL. The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yds/Att) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season (NFL website).

$$\begin{array}{lcc}\text { Team } & \text { Yds/Att } & \text { WinPct } \\ \text { Arizona Cardinals } & 6.5 & 50 \\ \text { Atlanta Falcons } & 7.1 & 63 \\ \text { Carolina Panthers } & 7.4 & 38 \\ \text { Chicago Bears } & 6.4 & 50 \\ \text { Dallas Cowboys } & 7.4 & 50 \\ \text { New England Patriots } & 8.3 & 81 \\ \text { Philadelphia Eagles } & 7.4 & 50 \\ \text { Seattle Seahawks } & 6.1 & 44 \\ \text { St. Louis Rams } & 5.2 & 13 \\ \text { Tampa Bay Buccaneers } & 6.2 & 25\end{array}$$

e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was 6.2. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For the 2011 season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs.

Write a one-sentence definition of the term "genotype." Do the same for "phenotype." Does the phenotype of an organism automatically change when a change in genotype occurs? Why or why not? Can phenotype change without a change in genotype? In both cases, give examples to support your answer.

To measure the index of refraction of some small transparent chips of plastic of irregular shape, a physicist places the chips in a glass beaker full of water. She then gradually adds sucrose to the water until the chips suddenly become nearly invisible. Explain why a measurement of the index of refraction of the sucrose solution then yields the index of refraction of the chips of plastic.

Measure the item to the unit in parentheses.

the width of your index finger (millimeters). ___________________________________

Give a big-O estimate for each of these functions. For the function $g$ in your estimate $f (x)$ is $O(g(x))$, use a simple function $g$ of smallest order.

a) $(n^3+n^2 \log n)(\log n+1) + (17 \log n+19)(n^3+2)$
b) $(2^n + n^2)(n^3 + 3^n)$
c) $(n^n + n2^n + 5^n)(n! + 5^n)$