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

Question 7.9

(a) Hypothesises are :

H0 : p < =0.3

Ha : p > 0.3

(b) Here when the true survival rate is 25% then there would be type I error as the null hypothesis is correct and we have to reject it.

so Pr(Type I error) = BIN (X >= 8; 15; 0.25) = 1 - BIN(X < 8; 15; 0.25) = 1 - 0.9827 = 0.0173

(c) Here if the true survivial rate = 0.30 then also the error would be type I error as the null hypothesis is correct here and we have to reject it.

Pr(Type I error) = BIN (X >= 8; 15; 0.30) = 1 - BIN(X < 8; 15; 0.30) = 1 - 0.9500 = 0.05

(d) Here if the true survivila rate = 0.40 then the error would be type II error as the nulll hypotheiss is false here and we will failed to reject it.

Pr(Type II error) = BIn (X < 8; 15 ; 0.40) = 0.787

(e) here level of significance alpha =BIN (X >= 8; 15; 0.30) = 1 - BIN(X < 8; 15; 0.30) = 1 - 0.9500 = 0.05

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