To test the effectiveness of a new drug, a researcher gives one group of individ

Question

To test the effectiveness of a new drug, a researcher gives one group of individuals the new drug and another group a placebo. The results of the study are shown here. At alpha= 0.5, can the researcher conclude that the drug is effective? Use P-value method.

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State the hypotheses and identify the claim with the correct hypothesis.

H0: Effectiveness is (dependent or independent) of whether the individual received the drug. Claim or Not Claim

H1: Effectiveness (depends/ does not depends) on whether the individual received the drug. (Claim or not claim)

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Explanation / Answer

For the group receiving the actual drug, 32 out of the total 41 showed that drug is effective.

So, p1 = 32/41 = 0.78

For the group receiving the placebo, 12 out of the total 30 showed that drug is effective.

So, p2 = 12/30 = 0.40

If the drug is not effective, then p1=p2, else p1>p2

So, the hypotheses are stated as:

H0 : p1-p2 = 0

Ha : p1-p2 > 0

Next, we calculate the pooled sample proportion, p = (p1n1+p2n2)/(n1+n2) = (32+12)/(41+30) = 0.619

Calculate the standard error of sampling distribution difference between two proportions, p' as follows:

p' = ( ( p*(1-p) )/( (1/n1) + (1/n2) ) )0.5 = ( (0.619*(1-0.619))/( (1/41) + (1/30) ) )0.5 = 2.021

Calculating the z-score: z = (p1-p2)/p' = (0.78-0.40)/2.021 = 0.188

The p-value for this z-score is:

pz = 0.425

Given aplha = 0.5

Since pz<alpha, so null hypothesis is rejected.

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