Question

Hemoglobin (g/100mL) was measured twice in 20 pregnant women. A first measurement was taken at 1-3 weeks prepartum whereas the second measurement was taken at 2-6 days postpartum (the data is provided below).

Part A. What is the absolute value of the t-test statistic for testing whether there is any change in mean hemoglobin levels between prepartum and postpartum women?

Part B. What is the degrees of freedom for this particular test in Part A?

a. 20

b. 38

c. 19

d. 25.6

Part C. What would you conclude from the corresponding t-test?

a. Mean hemoglobin decreases from prepartum to postpartum stages in women (P=0.02)

b. Mean hemoglobin decreases from prepartum to postpartum stages in women (P=0.04)

c. There is no evidence of a mean difference between prepartum and postpartum stages (P>0.05)

Part D. Suppose a hospital will not pursue any intervention measures if they believe that the true change in hemoglobin levels between prepartum and postpartum stages falls within +/- 2g/100mL; in other words, they feel the two stages are effectively equivalent for mean hemoglobin levels if the true mean difference falls within +/- 2g/100mL. Does this dataset provide proof of equivalence using a = 0.05?  

a. Yes based on a confidence interval of [0.18,186]

b. Yes based on a confidence interval of [0.20,1.84]

c. No based on a confidence interval of [0.32,1.72]

d. No based on a confidence interval of [0.03,2.01]

e. Yes based on a confidence interval of [0.32,1.72]

Data:

	woman	hemopre	hemopost
	1	13.63	12.53
2	2	15.17	12.77
3	3	13.1	13.8
4	4	13.82	12.22
5	5	12.31	11.51
6	6	13.09	13.49
7	7	12.62	9.82
8	8	11.29	7.49
9	9	13.45	8.85
10	10	12.8	15.2
11	11	13.15	10.05
12	12	13.74	14.04
13	13	12.48	13.38
14	14	13.23	13.13
15	15	12.85	11.45
16	16	13.31	12.71
17	17	13.31	11.21
18	18	14.96	13.96
19	19	13.21	14.81
20	20	13.35	12.05

Answer 1

Part A. What is the absolute value of the t-test statistic for testing whether there is any change in mean hemoglobin levels between prepartum and postpartum women?
2.531

Part B. What is the degrees of freedom for this particular test in Part A?
c. 19

Part C. What would you conclude from the corresponding t-test?

a. Mean hemoglobin decreases from prepartum to postpartum stages in women (P=0.02)

Part D. Suppose a hospital will not pursue any intervention measures if they believe that the true change in hemoglobin levels between prepartum and postpartum stages falls within +/- 2g/100mL; in other words, they feel the two stages are effectively equivalent for mean hemoglobin levels if the true mean difference falls within +/- 2g/100mL. Does this dataset provide proof of equivalence using a = 0.05?

a. Yes based on a confidence interval of [0.18,186]

The detailed solution is given below

Confidence interval.