Q1) Multiple myeloma or blood plasma cancer is classified by increased blood vessel formulation in bone marrow that is a prognostic factor in survival.  One treatment approach utilized for multiple myeloma is stem cell transplantation with patient's own stem cells.  Following data represent bone marrow micro vessel density for sample of 7 patients who had complete response to stem cell transplant as measured by blood and urine tests.  2 measurements were taken:  first immediately prior to stem cell transplant, and second at the time of complete response. 

1) If we want to find out if mean bone marrow microvessel density is higher before stem cell transplant than after the stem cell transplant, null hypothesis would be

i) H0: µd = 0

ii) H0: µd > 0

iii) H0: µd < 0

iv) H0: µd ≠ 0

2) If we are interested in finding if mean bone marrow micro vessel density is higher before stem cell transplant than after stem cell transplant, alternative hypothesis would be

i) H1: µd = 0

ii) H1: µd > 0

iii) H1: µd ≤ 0

iv) H1: µd ≠ 0

3) Carry out an suitable test of hypothesis to find out if there is evidence, at.05 level of significance, to support claim that mean bone marrow micro vessel density is higher before stem cell transplant than after stem cell transplant? Determine the value of sample test statistic?

i) z = 1.8424

ii) t = 1.8424

iii) t = 2.7234

iv) p = 2.7234

4) Find out the p-value associated with test of hypothesis you conducted?

i) p = .057403

ii) p = .114986

iii) p = .942597

iv) p = .885014

5) Mention the null and alternative hypotheses.

i) H0: µ = .79, H1: µ > .79

ii) H0: p = .79, H1: p ≠ .79

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

iv) H0:  = .79, H1:   > .79