Question

Multiple myeloma, or plasma cancer, is characterized by increase blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells.

The data is listed bellow:

Patient	Before	After
1	158	284
2	189	214
3	202	101
4	353	227
5	416	290
6	426	176
7	441	290

a) At alpha 0.05 level of significance, is there evidence that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?

Use the Excel output to answer the questions below:

Paired t Test
Data
Hypothesized Mean Difference	0
Level of significance	0.05
Intermediate Calculations
Sample Size	7
DBar	86.1429
Degrees of Freedom	6
SD	123.7005
Standard Error	46.7544
t Test Statistic	1.8425
Upper-Tail Test
Upper Critical Value	1.9432
p-Value	0.0575

a) What is the null hypothesis?

b) What is the correct t-statistic?

c) What is the correct decision rule?

d) What is the correct conclusion?

e) Using only the p-value, what is the conclusion?

Answer 1

a) At alpha 0.05 level of significance, is there evidence that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?

Answer: At alpha 0.05 level of significance, there is not sufficient evidence that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, because the p-value for the test is given as 0.0575 which is greater than the alpha value or significance level 0.05, so we do not reject the null hypothesis.

a) What is the null hypothesis?

Answer: Null hypothesis: H₀: The mean bone marrow microvessel density is same before the stem cell transplant and after the stem cell transplant.

b) What is the correct t-statistic?

Answer: t-statistic = 1.8425

c) What is the correct decision rule?

Answer: Decision rule: Reject H₀ if test statistic t > 1.9432.

d) What is the correct conclusion?

Answer: For the given test, test statistic value is less than critical value 1.9432, so we do not reject the null hypothesis.

e) Using only the p-value, what is the conclusion?

Answer: The p-value for the test is given as 0.0575 which is greater than the alpha value or significance level 0.05, so we do not reject the null hypothesis.