A manufacturer withdrew Drug V from the market after a study revealed that its u

Question

A manufacturer withdrew Drug V from the market after a study revealed that its use was associated with an increase in the risk of heart attack. The experiment was placebo-controlled, randomized, and double-blind. Out of 1253 people taking Drug V there were 37 heart attacks, and out of 1271 people taking the placebo, there were 28 heart attacks. Perform a hypothesis test to test whether those who take Drug V have a greater rate of heart attack than those who take a placebo. Use a level of significance of .01. Can we conclude that Drug V causes an increased risk of heart attack?

Explanation / Answer

Solution:

p1 = 37/1253 = 0.02952

n1 = 1253

p2 = 28/1271 = 0.02202

n2 = 1271

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1< P2

Alternative hypothesis: P1 > P2

Note that these hypotheses constitute a one tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.02575

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = 0.00630

z = (p1 - p2) / SE

z = 1.1904

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a one-tailed test,

Thus, the P-value = 0.117

Interpret results. Since the P-value (0.117) is more than the significance level (0.01), we have to accept the null hypothesis.

From this we can conclude that we do not have sufficient evidence in the favor of the claim that Drug V causes an increased risk of heart attack.

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