3. A company claims that its medicine,Brand A, provides faster pain relief than another company’s medicine, Brand B. A researcher tested both brands of medicine on two groups of randomly selected patients. The results of the medical tests are given in the following table. The mean and standard deviation of relief times are in minutes.
Brand A B
Sample Size 25 22
Mean Relief Times 44 49
Standard Deviation of Relief Times 11 9
(a) Define μ1 and μ2 in the context of the problem.
(b) What is the point estimate for μ1 − μ2?
(c) Construct a 99% confidence interval for μ1 − μ2. (Use d.f.=40 to read the t-table value.)
(d)Perform a hypothesis test to test the claim: mean relief time for Brand A is less than that for Brand B
.
(i) Formulate the null and alternative hypotheses.
(ii) State the appropriate test statistic and its distribution.
(iii) Compute the test statistic assuming the null hypothesis is true.
(iv) At α=0.01 level of significance, state your conclusion in the context of this study.
