7.9 The survival rate of a cancer using an existing medication is known to be 30

Question

7.9  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  be the number of cures out of the 15 patients.  Suppose the rejection region is {X>8}

a.)State the testing hypotheses.

b.)Determine the type of error that can occur when the true survival rate is 25%.  

Find the error probability

c.)Determine the type of error that can occur when the true survival rate is 30%.  Find the error probability.

d.)Determine the type of error that can occur when the true survival rate is 40%.  Find the error probability.

e.)What is the level of significance?

Explanation / Answer

(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 survivial 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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