# Hypothesis testing problems

See the attachment for proper formatting of tables and special characters.

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. Use these data to answer questions 1 through 5.

(see attached file)

1. If we wish to determine if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the null hypothesis would be

A) H0: ud = 0

B) H0: ud > 0

C) H0: ud < 0

D) H0: ud ≠ 0

2. If we are interested in determining if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the alternative hypothesis would be

A) H1: ud = 0

B) H1: ud > 0

C) H1: ud ≤ 0

D) H1: ud ≠ 0

3. Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?

A) z = 1.8424

B) t = 1.8424

C) t = 2.7234

D) p = 2.7234

4. What is the p-value associated with the test of hypothesis you conducted?

A) p = .057403

B) p = .114986

C) p = .942597

D) p = .885014

5. At the .05 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?

A) no

B) yes

C) It is impossible to determine

Consider this scenario in answering questions 6 through 8. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

6. State the null and alternative hypotheses.

A) H0: u = .79, H1: u > .79

B) H0: p = .79, H1: p ≠ .79

C) H0: p = .79, H1: p > .79

D) H0: p = .79, H1: p > .79

7. Compute the z or t value of the sample test statistic.

A) z = 0.69

B) t = 1.645

C) z = 1.96

D) z = 0.62

8. What is your conclusion?

A) Do not reject H0

B) Reject H0

C) Cannot determine

D) More seniors are going to college

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Use these data to answer questions 9 through 11.

(see attached file)

9. What is the equation for the least squares line?

A) Y = 2.63 + 0.724x

B) Y = 1.45 + 0.724x

C) Y = 1.45 + 0.074x

D) Y = 2.63 - 0.174x

10. Compute the coefficient of determination.

A) 0.8270

B) 0.6839

C) 0.3081

D) 0.0009

11. Construct a 95% prediction interval estimate for the weekly sales, in hundreds of dollars, for a store with 8 feet of shelf space devoted to pet food.

A) 2.86 < y < 6.23

B) 1.31 < y < 2.77

C) -0.131 < y < 1.84

D) 1.54 < y < 4.24

A market research study was conducted to compare three different brands of antiperspirant. The results of the study are summarized below. Use a 5% level of significance and test the claim that opinion is independent of brand. Use these data to answer questions 12 and 13.

(see attached file)

12. What is the value of the sample test statistic?

A) x^2 = 19.00

B) x^2 =9.49

C) F = 0.10

D) x^2 = 11.91

13. What is your conclusion?

A) Opinion and Brand are independent

B) Opinion and Brand are not independent

C) Cannot determine

Customer base data for sporting goods stores

(see attached file)

The data in the above worksheet “CustomerData” includes the monthly sales totals from a random sample of 38 stores in a nation-wide chain of sporting goods stores. All stores in the chain are approximately the same size and carry essentially the same merchandise. Information—as described in the comments in each column—is also provided in this dataset regarding the customer base for each of the 38 stores in the sample. Use these data to answer questions 14 through 18.

14. Assuming a linear relationship exists, formulate a simple linear regression model that estimates the relationship between monthly sales (Y) and median family income (X).

A) Y = 39.17 + 299876.81(X)

B) Y = 299876.81 + 39.17(X)

C) Y = 785476.90 + 43.96(X)

D) Y = 14.07 + 278756.44(X)

15. Compute the coefficient of determination. Enter it, rounded to four decimal places in the blank. ___________

16. At the a = .05 level of significance, is there evidence of a statistically significant linear relationship between monthly sales and median family income?

A) No

B) Yes

C) It cannot be determined

17. Derive a 95% confidence interval estimate for predicting the monthly sales associated with a store located in an area where the median family income is $35000. Place your limits, rounded to the nearest dollar, in the blanks. Lower limit in the first blank; upper limit in the second blank. Do not use dollar signs, commas, or other punctuation in your responses.

Lower limit = _________________

Upper limit = _________________

18. With respect to the response variable, monthly sales, which predictor variable among those given in the worksheet CustomerData, provides the most explanatory power?

A) Age

B) Growth

C) Income

D) HS

E) College

NFL salaries and bonuses 2000 season

(see the attachment)

Data regarding the salaries and bonuses received by the nearly 1800 players in the National Football League during the 2000 season are provided above. Using these data, perform an appropriate test of hypothesis, at the a = .05 level of significance, to determine whether compensation for players in the NFL is dependent on the team for which they play.

19. What is the value of the sample test statistic?

A) x^2 = 113.15

B) x^2 = 160.47

C) p = 0.0001

D) x^2 = 224.78

20. What is your conclusion?

A) Salary and team membership are independent

B) Salary and team membership are dependent

C) Cannot determine

D) The Pittsburgh Steelers are the best franchise in the NFL

#### Solution Summary

The solution provides step by step method for the calculation of test statistic . Formula for the calculation and Interpretations of the results are also included.