Suppose that we want to evaluate the role of intravenous pulse cyclophosphamide (IVCP) infusion in the management of nephrotic syndrome in children with steroid resistance. Children were given a monthly infusion of IVCP in a dose of 500 to 750 mg/m2. The following data (source: S. Gulati and V. Kher, "Intravenous pulse cyclophosphamide-A new regime for steroid resistant focal segmental glomerulosclerosis," Indian Pediatr. 37, 2000) represent levels of serum albumin (g/dL) before and after IVCP in 14 randomly selected children with nephrotic syndrome.
|
Pre-IVCP
|
2.0
|
2.5
|
1.5
|
2.0
|
2.3
|
2.1
|
2.3
|
1.0
|
2.2
|
1.8
|
2.0
|
2.0
|
1.5
|
3.4
|
|
Post-IVCP
|
3.5
|
4.3
|
4.0
|
4.0
|
3.8
|
2.4
|
3.5
|
1.7
|
3.8
|
3.6
|
3.8
|
3.8
|
4.1
|
3.4
|
Assuming that the samples come from a normal distribution:
(a) Test whether the mean Pre-IVCP is less than the mean Post-IVCP at α = 0.05. Assume that the variances are equal.
(b) Test for the equality of the variances at α = 0.05.
(c) In parts (a) and (b), we assumed that the samples are independent. Now, we feel this assumption is not reasonable. Assuming that the difference of each pair is approximately normal, test that the mean Pre-IVCP is less than the Post-IVCP at α = 0.05.