Question

A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 21 subjects were assigned randomly to the treatment group, and received the new experimental drug. The other 23 subjects were assigned to the control group, and received a standard, well known treatment. After a suitable period of time, the reduction in blood pressure for each subject was recorded. A summary of these data is: Treatment n=21 xbar=23.48 s=8.01 Old Drug n=23 xbar=18.52 s=7.15 The researcher suspects that the new drug results in greater average reduction in blood pressure than the old drug does.

The P-value for the test described in (again, using Option 2 for degrees of freedom) is:

A. larger than 0.05.

B. between 0.025 and 0.05.

C. between 0.04 and 0.05.

D. between 0.02 and 0.025.

Answer 1

The correct answer is D. The researcher suspects that the new drug results in greater average reduction in blood pressure than the old drug. The P-value for the test described in (again, using Option 2 for degrees of freedom) is between 0.02 and 0.025.

Step-by-step explanation:

To test the hypothesis that the new drug results in a greater average reduction in blood pressure than the old drug, we can perform a two-sample t-test. The null hypothesis is that there is no difference in the average reduction between the two drugs, while the alternative hypothesis is that the new drug has a higher average reduction.

The test statistic is calculated as:

T = (xbar1 - xbar2) / sqrt((s1^2/n1) + (s2^2/n2))

where xbar1 and xbar2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes. Using the given data:

T = (23.48 - 18.52) / sqrt((8.01^2/21) + (7.15^2/23)) ≈ 2.03

The degrees of freedom for this test is the smaller sample size minus 1, so df = 21 - 1 = 20. Using a t-distribution table or statistical software, we can find the p-value associated with this test statistic and degrees of freedom. Based on the information given, the P-value for the test is between 0.02 and 0.025, therefore the correct answer is D.