Question

1. Suppose you are studying the effects of a new drug on diastolic blood pressure. Twelve patients were enrolled in the study. The patients were asked to takethe old drug for 6 months, and then the new drug for the remaining 6 months. The blood pressure measurements are given in the following table.

	Diastolic blood pressure, mmHg
New drug	90	92	85	88	94	86	96	96	97	88	94	93
Old drug	92	96	95	93	90	89	94	98	99	94	94	95

1. (0.5 p)Are the data paired or unpaired? Justify your answer.
2. (0.5 p)Find the 95% confidence interval for the difference of the means.
3. (1 p)Perform the hypothesis test (significance level α = 0.05). Is the new drug more effective compared to the old drug?

Answer 1

Solution:

a) Yes, the data is paired because we have the same group of individuals tested for two treatments (new drug and old drug)

b) The 95% confidence interval for the difference of the means is:

c. Perform the hypothesis test (significance level α = 0.05). Is the new drug more effective compared to the old drug?

Answer: The null and alternative hypothesis is:

Under the null hypothesis, the test statistic is:

The left-tailed critical value at 0.05 significance level for df = n - 1= 11 is:

Since the test statistic lies beyond the critical value, we, therefore, reject the null hypothesis and there is sufficient evidence to conclude that the new drug is more effective compared to the old drug.