Anjum: Sorry for the confusion. You want to find another distribution where the SAMPLE you took has the same mean and variance. For instance, imagine getting a sample and it happens to have come from a chi-squared (just for illustration) distribution. If you assume Ho is true, you will do your stuff according to parts a and b to get a locations for c1,c2 and distribution of r(x). Compare that to what you would get if you had calculated locations for c1 and c2 (and therefore r(x)) assuming the same points had come from a chi-squared distribution. Is that helpful?