Question

Imagine that a researcher develops a new cancer drug that shrinks tumors, which she measures using an MRI. The researcher needs to determine if the new drug performs differently from, or the same as, the current gold-standard drug therapy which shrinks tumor diameter by an average of 0.1 mm. After performing an experiment to test the new drug on a group of 5747 cancer patients, the researcher analyzes the measurements of tumor shrinkage by using a one-sample 2-test for a mean at the significance level of a = 0.10, with power of 0.96. Assume that the researcher knows the standard deviation of tumor reduction is o = 2.5 mm, perhaps from previous studies with similar populations. Assuming that in fact the null hypothesis is true and that the new cancer drug shrinks tumors by the same amount as the gold-standard drug, what is the probability that the test will lead the researcher to this decision? Give the probability as a percentage to the nearest whole number.

Answer 1

here as nulll hypothesis is correct and we are not rejecting it , which means we are making a correct decision

P(not reject the null| null hypothesis is true) =1-P(reject null|null is true) =1-type I error =1-0.1 =0.9 ~ 90 %