Total 2005 CE0 compensation for the largest U.S. companies by revenue is reported in the following frequency distribution, along with some summary statistics. Total compensation includes salary, bonuses, stock and incentives, the potential value of stock options, and gains from stock options exercised.

$$\begin{array}{|l|c|} \hline \begin{array}{l} \text { Total Compensation } \\ \text { (in millions of \$) } \end{array} & \text { Frequency } \\ \hline \text { Less than } 5 & 43 \\ \hline 5 \text { up to } 10 & 65 \\ \hline 10 \text { up to } 15 & 32 \\ \hline 15 \text { up to } 20 & 38 \\ \hline 20 \text { or more } & 60 \\ \hline & n=238 \\ \hline \end{array}$$

Other summary statistics for CEO compensation (in millions of $) are as follows:$

$$\begin{array}{|c|c|c|c|c|} \hline \text { Mean } & \text { Median } & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} & \text { Skewness } & \text { Kurtosis } \\ \hline 19.03 & 11.02 & 27.61 & 5.26 & 35.53 \\ \hline \end{array}$$

$a. Conduct a goodness-of-fit test for normality of CEO compensation at the 1% significance level.

b. Conduct the Jarque-Bera test at the 1$ significance level.

c. Does total compensation of CEOs for the largest U.S. companies not follow the normal distribution?

You spend the day looking for hidden containers in a wooded area using a global positioning system (GPS). You park your car on the side of the road and then locate Container 1 and Container 2 before going back to the car. Does your path form a right triangle? Explain. Each unit of the grid represents 10 yards.

Jorge is a member of the student government at a large school with over 2500 students. The student government would like to recommend that students with part-time jobs be permitted to get a class credit in business. Knowing that Jorge is a good statistics student, the student government asked him to estimate the proportion of students at the school who have part-time jobs. Jorge is on the football team at his school and is thinking of asking everyone on the football team if they have a part-time job. Why might this give him a poor estimate of the actual proportion of students at his school with part-time jobs?

Statistics students were asked to go home and fill a 1-cup measure with raisin bran, tap the cup lightly on the counter three times to settle the contents, if necessary add more raisin bran to bring the contents exactly up to the 1-cup line, spread the contents on a large plate, and count the raisins. For the 13 students who chose Kellogg’s brand, the reported results were

23 33 44 36 29 42 31 33 61 36 34 23 24

Construct a 90 percent confidence interval for the mean number of raisins per cup. Show your work clearly.

In an article that appears on the web site of the American Statistical Association (www.amstat.org), Carlton Gunn, a public defender in Seattle, Washington, wrote about how he uses statistics in his work as an attorney. He states: I personally have used statistics in trying to challenge the reliability of drug testing results. Suppose the chance of a mistake in the taking and processing of a urine sample for a drug test is just 1 in 100. And your client has a “dirty” (i.e., positive) test result. Only a 1 in 100 chance that it could be wrong? Not necessarily. If the vast majority of all tests given—say 99 in 100—are truly clean, then you get one false dirty and one true dirty in every 100 tests, so that half of the dirty tests are false. Define the following events as TD = event that the test result is dirty, TC = event that the test result is clean, D = event that the person tested is actually dirty, and C = event that the person tested is actually clean. a. Using the information in the quote, what are the values of b. Use the law of total probability to find P(TD) . c. Use Bayes’ rule to evaluate P(C \ TD) . Is this value consistent with the argument given in the quote? Explain.

$$\begin{array}{ll}{\text { i. } P(T D | D)} & {\text { iii. } P(C)} \\ {\text { ii. } P(T D | C)} & {\text { iv. } P(D)}\end{array}$$

The numbers y (in thousands) of hairdressers and cosmetologists in the United States for the years 1994 through 2002 are shown in the table. (Source: U.S. Bureau of Labor Statistics)

$$\begin{array}{|c|c|} \hline \text { Year } & \begin{array}{c} \text { Number of hairdressers and } \\ \text { cosmetologists, } y \end{array} \\ \hline 1994 & 753 \\ 1995 & 750 \\ 1996 & 737 \\ 1997 & 748 \\ 1998 & 763 \\ 1999 & 784 \\ 2000 & 820 \\ 2001 & 854 \\ 2002 & 908 \\ \hline \end{array}$$

Use a graphing utility to graph the model in the same viewing window as the scatter plot. How well does the model fit the data?

Find the potential misuse (or abuse) of statistics in the following.
a. An ad reads, “Work from home. Earn an average of $500 weekly.”
b. The same five questions appear in the same order on all the questionnaires printed for Acme Foods.
c. A company spokesperson made the claim that 3 out of 4 dentists prefer their dental products.
d. A news host brought the discussion on an education topic to viewers at home by asking them to send a text message containing a yes/no response to the toll free number displayed on their screen.
e. A survey question reads, “Do you support the district’s decision to fund the school’s much-needed science facility?”

For each function: i Find any stationary points and determine the nature of the points. ii State the intervals in which the function increases. iii State the intervals in which the function decreases. iv Confirm your answers graphically, and state whether the points found in part $\mathrm{i}$ are local or global extrema.

$y=x+\frac{1}{x-1}$

The number of car accidents on a particular stretch of highway seems to be related to the number of vehicles that travel over it and the speed at which they are traveling. A city alderman has decided to ask the county sheriff to provide him with statistics covering the last few years, with the intention of examining these data statistically so that he can (if possible) introduce new speed laws that will reduce traffic accidents. Using the number of accidents as the dependent variable, he obtains estimates of the number of cars passing along a stretch of road and their average speeds (in miles per hour). The observations for 60 randomly selected days were recorded. Is the model valid?

Match the terms with the definitions. Some terms may not be used.

a. balanced fund

b. global fund

c. growth and income fund

d. growth fund

e. income fund

f. index fund

g. load

h. money market fund

i. net asset value

j. prospectus

__ The sales fee charged for buying mutual funds

Choose the best answer. Which constitutes baseline data on the effects of humans on natural ecosystems? (a) concentrations of atmospheric $\mathrm{CO}_{2}$ before humans existed (b) current rates of species extinction (c) global rate of freshwater consumption from 1900 to 2010 (d) average plant productivity on a remote island uninhabited by humans

Students attending the University of Florida can select from 130 major areas of study. A student’s major is identified in the registrar’s records with a two-or three-letter code (for example, statistics majors are identified by STA, math majors by MS). Some students opt for a double major and complete the requirements for both of the major areas before graduation. The registrar was asked to consider assigning these double majors a distinct two- or three-letter code so that they could be identified through the student records’ system. What is the maximum number of possible double majors available to University of Florida students?

Distinguish between a carbon-tax and a cap-andtrade strategy for reducing carbon dioxide and other so-called greenhouse gases (that are believed by many scientists to be causing global warming). Which of the two strategies do you think would have the most political support in an election in your home state? Explain your thinking.

Match the terms with the definitions. Some terms may not be used.

a. balanced fund

b. global fund

c. growth and income fund

d. growth fund

e. income fund

f. index fund

g. load

h. money market fund

i. net asset value

j . prospectus

__ The market price for a share of a mutual fund