Multiple myeloma or blood plasma cancer is characterized by increased blood vess
ID: 3157281 • Letter: M
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
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?
A.No
B.Yes
C.Cannot Determine
Explanation / Answer
The differences are (before - after):
-126
-25
101
126
126
250
151
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
At level of significance = 0.01
As we can see, this is a right tailed test.
Calculating the standard deviation of the differences (third column):
s = 101.5579772
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 38.38530732
Calculating the mean of the differences (third column):
XD = 86.14285714
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = 2.244162237
As df = n - 1 = 6
Then the critical value of t is
tcrit = + 3.142668403
Also, using p values,
p = 0.032984229
As t < 3.143, and P > 0.01, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Hence,
OPTION A: NO. [ANSWER]
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