a. At the 0.01 level of significance, is there evidence that the mean microvessel density is higher before the stem cell transplant than after the stem cell transplant? Let μ1 be the mean density before the transplant and let μ2 be the mean density after the transplant. State the null and alternative hypotheses. Choose the correct answer below.
A. H0: μD = 0 (where μD = μ1 - μ2)
H1: μD ≠ 0
B. H0: μD ≤ 0 (where μD = μ1 - μ2)
H1: μD > 0
C. H0: μD = 0 (where μD = μ1 - μ2)
H1: μD > 0
D. H0: μD ≥ 0 (where μD = μ1 - μ2)
H1: μD < 0
E. H0: μD ≤ 0 (where μD = μ1 - μ2)
H1: μD > 0
F. H0: μD ≠ 0 (where μD = μ1 - μ2)
H1: μD = 0
The test statistic =
(Round to two decimal places as needed.)
The p-value is
(Round to three decimal places as needed.)
Since the p-value is the value of α, There is evidence to conclude that the mean microvessel density is higher before the stem cell transplant than after the stem cell transplant.
b. Interpret the meaning of the p-value in (a). Choose the correct answer below.
A. The p-value is the probability of not rejecting the null hypothesis when it is false.
B. The p-value is the probability of obtaining a sample mean difference of 94.57 or more if the population mean densities both before and after the transplant are the same.
C. The p-value is the probability of obtaining a sample mean difference of 94.57 or more if the population mean densities both before and after the transplant are different.
d. What assumption is necessary about the population distribution in order to perform the test in (a)?
A. It must be assumed that the distribution of the differences between the measurements is approximately uniform.
B. It must be assumed that the distribution of the differences between the measurements is skewed.
C. It must be assumed that the distribution of the differences between the measurements is approximately normal.