Question

The following experiment was carried out to evaluate a drug for the prevention of heart attacks. The subjects were 3,900 middle-aged men with heart trouble. Out of these men, 1,100 were assigned at random to receive the drug, and the remaining 2,800 were given a placebo. The subjects were followed for five years. In the group that received the drug, there were 220 deaths; in the control group, 2 there were 588 deaths. The 220 is 20% of the treatment group and the 588 is 21% of the control group. Someone argues as follows: “A one-percentage-point difference may not seem like much, but 1% of a million, for example, is 10,000. The drug will save tens of thousands of lives.” Do you agree or disagree with the statement? Explain and show mathematically.

Answer 1

We disagree with the statement.

Explanation:
H0: Null Hypothesis: p1 p2 (Drug is not effective)

HA: Alternative Hypothesis: p1 < p2 (Drug is effective)

n1 = 1100

1 = 220/1100 =0.20

n2 = 2800

2 = 588/2800 = 0.21

Pooled Proportion is given by:

Test Statistic is given by:

Take = 0.05

From Table, critical value of Z = - 1.64.

Since calculated value of Z = - 0.693 is greater than critical value of Z = - 1.64, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that Drug is effective.

We have statistically proved that the one-percentage-point difference is not due to the effectiveness of the drug and it is due to only statistical variation of data. Thus, we disagree with the statement: “A one-percentage-point difference may not seem like much, but 1% of a million, for example, is 10,000. The drug will save tens of thousands of lives.”