Question

A pharmacutical company is testing a new allergy medication. They will consider the drug to be effective if the percentage of patients in the treatment group whose symptoms get better is 15% more than the percentage of patients in the control group whose symptoms get better. For example, if 10% of patients in the control get better, and 30% of patients in the treatment group get better, they will consider the drug to be effective, since 30% - 10% = 20% > 15%.

After collecting data from 32 subjects who received the medication and 32 who did not, they find that a 95% confidence interval for the difference in the treatment and control group is (15%, 16%).

Interpret these findings: Select your answer from one of the following options.

• a.The company cannot determine whether the drug is effective, but the confidence interval includes 15%, so they should collect more data.
• b.The company cannot determine whether the drug us effective from this sample, but the confidence interval includes 15%, so they should collect more data.
• c.The company should consider the drug effective, because the average difference in the treatment and control is greater than 15%.

Answer 1

The pharmaceutical company is considering the drug as being effective when the percentage of patients in the treatment group who get better is at least 15% more than the patients who get better in the control group.

Let be the percentage of patients in the control group who get better and be the percentage of patients in the treatment group who get better.

Hence, the rule of the company to consider the treatment to be effective is when:

Now, they have collected data from 64 subjects. Of these 64, 32 belonged to the control group and 32 belonged to the treatment group and hence were administered the drug. They then checked the percentage difference between the two groups. They got a 95% Confidence Interval for the difference of (15%, 16%). This implies that the difference between treatment and control group recoveries is between 15% and 16% with 5% uncertainty. Hence, the probability that the difference is less than 15% is 5/2 = 2.5%.

Hence, they can be confident that their drug is effective.

Therefore, the correct answer is c.