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According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40 taxpayers and finds the standard deviation of the time to prepare, copy, and electronically file form 1040 is 80 minutes.

a) What assumption or assumptions do you need to make about the shape of the population?
b) What is the standard error of the mean in this example?
c) What is the likelihood the sample mean is greater than 320 minutes?
d) What is the likelihood the sample mean is between 320 and 350 minutes?
e) What is the likelihood the sample mean is greater than 350 minutes?

General K. is concerned about sexually transmitted disease (STD) among the troops. In random inspection of 100 soldiers, 31 were found to have a venereal disease. To reduce the incidence, soldiers were shown an educational film on preventing STDs. In a second inspection of 200 soldiers, 43 had STDs. Calculate the following statistics.
Soldiers with STDs
1st Inspection 2nd Inspection
What is the Sample proportion (mean)? 31 43
What is the Standard deviation?
What is the Standard error of the proportion estimate?
What is the Overall standard error ?
What is the t-score?
What do these statistics suggest?

Kimble Products:
Is There a Difference In the Commissions?

At the January national sales meeting, the CEO of Kimble Products was questioned extensively regarding the company policy for paying commissions to its sales representatives.The company sells sporting goods to two major markets. There are 40 sales representatives who call directly on large volume customers, such as the athletic departments at major colleges and universities and professional sports franchises. There are 30 sales representatives who represent the company to retail stores located in shopping malls and large discounters such as Kmart and Target.

Upon his return to corporate headquarters, the CEO asked the sales manager for a report comparing the commissions earned last year by the two parts of the sales team. The information is reported on the right. Write a brief report. Would you conclude that there is a difference? Be sure to include information in the report on both the central tendency and dispersion of the two groups.

A recent article in Business Week listed the “Best Small Companies.” We are interested in the current results of the companies’ sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

Sales Earnings Sales Earnings
Company ($ millions) ($ millions) Company ($ millions) ($millions)
Papa John’s International $89.2 $4.9 Checkmate Electronics $17.5 $ 2.6

Applied Innovation 18.6 4.4 Royal Grip 11.9 1.7

Integracare 18.2 1.3 M-Wave 19.6 3.5

Wall Data 71.7 8.0 Serving-N-Slide 51.2 8.2

Davidson Associates 58.6 6.6 Daig 28.6 6.0

Chico’s Fas 46.8 4.1 Cobra Golf 69.2 12.8

Let sales be the independent variable and earnings be the dependent variable. Each question must be answered in its entirety.

a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Interpret your findings in parts b and c.
e. Determine the regression equation.
f. For a small company with $50.0 million in sales, estimate the earnings

1.Senator Hayes is considering a a run for the U.S. presidency, but she is only 35 years of age, which is the minimum required age. While investigating this issue, she finds the ages of past presidents when they were inaugurated, and those ages are listed below. Using the ages listed find the (a) mean; (b) median; (c) mode; (d) midrange; (e) range; (f) standard deviation; (g) variance; (h)Q1; (I) Q3; (J)P10-

57 61 57 57 58 57 61 54 68 51 49 64 50 48

65 52 56 46 54 49 51 47 55 55 54 42 51 56

55 51 54 51 60 62 43 55 56 61 52 69 64 46

54

2.

(a) John F. kennedy was 43 years of age when he was inaugurated. Using the results from exercise 1, convert his age to a z score.

(b) Is Kennedy’s age of 43 years “unusual”? Why or why not?

(c) Using the range rule of thumb, identify any other listed ages that are unusual.

(D) Although the list of ages does not include an age of 35 years, would that age be unusual? Is it likely that a presidential candidate of age 35 would find that his or her age would be a major campaign issue?

3. Frequency Distribution

Using the same ages listed in exercise Exercise 1, construct a frequency distribution. Use six classes with 40 as the lower limit of the first class, and use a class width of 5.

The production department of NDB Electronics wants to explore the relationship between the number of employees who assemble a sub-assembly and the number produced. As an experiment, two employees were assigned to assemble the sub-assemblies. They produced 15 during a one-hour period. Then four employees assembled them. They produced 25 a one-hour period. The complete set of paired observations follows.

Number of Assemblers One- Hour Production (units)

2 15
4 25
1 10
5 40
3 30

The dependent variable is production; that is assumed that the level of production depends upon the number of employees.

a. Draw a scatter diagram.
b. Based on the scatter diagram, does there appear to be any relationship between the number assemblers and production? Explain.
c. Compute the coefficient of correlation.
d. Evaluate the strength of the relationship by computing the coefficient of determination.