A drug is claimed to produce a cure to a certain disease in \(35 \%\) of people who have the disease. To test this claim a sample of 20 people having this disease is chosen at random and given the drug. If the number of people cured is between 4 and 10 inclusive the claim will be accepted. Otherwise the claim will not be accepted.
Write down suitable hypotheses to carry out this test.
Find the probability of making a Type I error.
The table below gives the value of the probability of the Type II error, to 4 decimal places, for different values of \(p\) where \(p\) is the probability of the drug curing a person with the disease.
P (cure)
0.2
0.3
0.4
0.5
P (Type II error)
0.5880
\(r\)
0.8565
\(s\)
Calculate the value of \(r\) and the value of \(s\).
Calculate the power of the test for \(p = 0.2\) and \(p = 0.4\)
Comment, giving your reasons, on the suitability of this test procedure.