Question

The survival rate of patients with a tumor using an existing medication is known to be 40%. A pharmaceutical company claims that the survival rate of a new drug is higher. The new drug is given to 20 patients to test for this claim. Let X be the number of cures out of the 20 patients. Suppose the rejection region is {X>=12). Compute the type of error that can occur when the survival rate is 50% (round off to second decimal place).

Answer 1

As we are given the true survival rate is indeed greater than 40% as it is given to be 50%.

Therefore the error that here could happen is Type II error which is the incorrect non rejection of the null hypothesis.

The probability of type II error here is computed as the probability of X < 12 when the true survival rate is 50% that is 0.5.

Therefore the probability here is computed using the binomial probability function here as:

Therefore 0.7483 is the required probability of type II error here.