Question

1. Imagine that you are testing an experimental drug that is supposed to reduce blood pressure but is suspected of inducing cancer. You administer the drug to a sample of rodents. Since you know that the tumor rate in this strain is 10% among untreated animals, your null hypothesis (the one which includes an equals sign) is that the tumor rate in treated animals is less than or equal to 10%, that is, the drug is safe, it does not cause tumors. The alternative hypothesis is that the tumor rate in treated animals is more than 10%, that is, the drug is not safe.                                                     

1. Describe the consequences of committing type I and Type II errors in context of this problem. Type I error= Type II error=
2. Which error is more serious? Type I or Type II?
3. Explain Why?

Answer 1

Let we denote tumor rate as p

Then the null hypothesis is : p0.1 i.e . The drug is safe

Alternative hypothesis is : p0.1 i.e. the drug is not safe

a) type I error = probability of rejecting the null hypothesis

when it is true that mean we reject the null hypothesis when it is safe.

Type II error = probability of accepting the null when it is false thet mean we accept the drug but actually it is false.

b) Here type I error is more serious .

c) if we fixed type I error by pre determined low level then we minimise the type II error and we get power function will increase.