Multiple myeloma or blood plasma cancer is characterized by increased blood vess

Question

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

A. 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 ?

B. 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 ?

C. 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?

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

E. 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?

Explanation / Answer

Solution:

A) Ho: d = 0(made no difference)
B) Ha: d # 0 (made a difference)

C) t(86) = (86-0)/(123.7/sqrt(7))
= 1.8394

D) p-value = 2*P(t > 1.8394 when df = 6)
= 2*tcdf(1.8394,100,6)
= 0.1155
E) Since the p-value is greater than 5%, fail to reject Ho.
Since we assumed d = 0 (no difference) we conclude the
procedure made no difference.

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