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 greaterthanorequalto 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

Part-a

Null hypothesis H0: p<=0.30 is to be tested against alternative hypothesis Ha: p>0.30.

Part-b

X follows Binomial distribution with n=15 and p=0.30

We have P(X>=8)=1-P(X<=7)

=0.05 using excel function =1-BINOMDIST(7,15,0.3,TRUE)

AS p-value=0.05, we reject the null hypothesis

If survival rate=0.25 actually then we concluded p>0.30 while in fact p<0.30, so we made Type-I error

Part-c

If survival rate=0.30 actually then we concluded p>0.30 while in fact p=0.30, so we made Type-I error

Part-d

If survival rate=0.40 actually then we concluded p>0.30 which is true so we did not make any error

Part-e

Level of significance is p-value=0.05

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