The survival rate of a cancer using an existing medication is known to be 30%. A

Question

The survival rate of a cancer using an existing medication is known to be 30%. A pharmaceutical company claims that the survival rate of a new drug is higher. The new drug is given to 15 patients to test for this claim. Let X be the number of cures out of the 15 patients. Suppose the rejection region is (X 2 8. a. State the testing hypotheses. b. Determine the type of error that can occur when the true survival rate is 25%. 7.9 Find the error probability Determine the type of error that can occur when the true survival rate is 30% Find the error probability. Determine the type of error that can occur when the true survival rate is 40%. Find the error probability d. e. What is the level of significance?

Explanation / Answer

X~ Binomial(15,p)

a. Null hypothesis: H0 : p=0.3

Alternative hypothesis : H1 : p>0.3

b. True p = 0.25

Error = (Accepting H0 when H0 is false) or ( Accepting H1 when H1 is false)

P(Error) = P(X<8) + P(X>=8) = 1

c. Error = Rejecting H0 when H0 is true, where p=0.3 = Type-1 error

P(Error) = PH0 (X>=8) = 0.05

d. Error = Accepting H0 when H0 is false, where p=0.4 = Type-2 error

P(Error) = PH1 (X<8) = 0.78

e. Level of significance = Type-1 error = 0.05

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