The standard error of the estimate, sest, is essentially the

1. Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response.

Patient

1

2

3

4

5

6

7

Before

158

189

202

353

416

426

441

After

284

214

101

227

290

176

290

At the .01 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?

2. A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the variation of the amount of money spent on lunches. The variance of nine business dinners was $6.12 and the variance of 12 business lunches was $0.87. What is the test value?

3. Q-Mart is interested in comparing its male and female customers. Q-Mart would like to know if the amount of money spent by its female charge customers differs, on average, from the amount spent by its male charge customers. To answer this question, an analyst collected random samples of 25 female customers and 22 male customers. Based on these samples, on average, the 25 women charge customers spent $102.23 and the 22 men charge customers spent $86.46. Moreover, the sample standard deviation of the amount charged by the 25 women was $93.393, and the sample standard deviation of the amount charged by the 22 men was $59.695. Using the procedure advocated by Bluman, at the 10% level of significance, is there sufficient evidence for Q-Mart to conclude that, on average, the amount spent by women charge customers differs from the amount spent by men charge customers.

4. In a simple linear regression analysis, the following sum of squares are produced: image1.png= 500 image2.png= 100 image3.png= 400 The proportion of the variation in Y that is explained by the variation in X is:

5. The standard error of the estimate, sest, is essentially the

6. An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost of apartments based on the size of the apartment. Data for a sample of 25 apartments in a particular neighborhood are provided. At the .05 level of significance determine if the correlation between rental cost and apartment size is significant.

Rent

Size

950

850

1600

1450

1200

1085

1500

1232

950

718

1700

1485

1650

1136

935

726

875

700

1150

956

1400

1100

1650

1285

2300

1985

1800

1369

1400

1175

1450

1225

1100

1245

1700

1259

1200

1150

1150

896

1600

1361

1650

1040

1200

755

800

1000

1750

1200

7. The regression line y' = -3 + 2.5 X has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be:

8. A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are the results of his random sampling. Can he conclude, at the 0.10 level of significance, that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree?

Pine trees

Spruce trees

Sample size

20

30

Mean trunk diameter (cm)

45

39

Sample variance

100

150

What is the test value for this hypothesis test?

What is the critical value?

9. The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Store

Shelf Space(X)

Weekly Sales(Y)

1

10

2.0

2

10

2.6

3

10

1.8

4

15

2.3

5

15

2.8

6

15

3.0

7

20

2.7

8

20

3.1

9

20

3.2

10

25

3.0

11

25

3.3

12

25

3.5

Find the equation of the regression line for these data. What is the value of the standard error of the estimate?

10. A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months are given in the file ILE_and_DLH.xlsx Treating ILE as the response variable, use regression to fit a straight line to all 18 data points. Approximately what percentage of the variation in indirect labor expenses is explained by the regression model you derived?

11. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation

15

12

3

12

28

6

8

2

percent change for CEO

6

17

-4

12

32

-1

7

2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the critical value that you would use to conduct this test of hypothesis?

12. Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at the annual company percentage increase in revenue versus the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

percent change for corporation

15

12

3

12

28

6

8

2

percent change for CEO

6

17

-4

12

32

-1

7

2

Do these data indicate that the population mean percentage increase in corporate revenue is greater than the population mean percentage increase in CEO salary? Use a 5% level of significance. What is the p-value associated with this test of hypothesis?

13. A special coating is applied to several scale model engine nacelle body shapes to determine if it reduces the drag coefficient. The following data are the drag coefficient before the coating is applied and after.

Model

#1

#2

#3

#4

#5

#6

Before

0.782

0.656

0.541

0.250

0.323

0.888

After

0.668

0.581

0.532

0.241

0.334

0.891

Perform a hypothesis test to determine if there is evidence at the 0.05 level of significance to support the claim that the coating reduces the drag coefficient. What is the test value for this hypothesis test?

What is the P-value for this hypothesis test?

What is your conclusion for this test?

13. When testing the equality of two population variances, the test statistic is the ratio of the population variances; namely image4.png.

14. In a simple regression analysis, if the standard error of estimate sest = 15 and the number of observations n = 10, then the sum of the residuals squared must be 120.

15. A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.

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