Reference no: EM132851877

Researchers are interested in the effectiveness of a newly-developed pain relief drug. They are interested in determining if it reduces perceived pain in patients following minor surgeries compared to a standard pain reliever. Previous research has shown that the standard pain reliever brings relief to patients in an average of 7.5 minutes following minor surgery, although the distribution of pain relief times is unknown in this surgical population. To test whether the new pain reliever works more quickly than the standard one, 75 patients with minor surgeries were given the new pain reliever and their times to relief were recorded. The experiment resulted in a sample mean of X =6.1 minutes and sample standard deviation s = 3.5 minutes. Use these data to answer the questions below.

a. Does the sample provide sufficient evidence to indicate, at the 5% level of significance, that the newly developed pain reliever is able to relieve perceived pain more quickly compared to the standard pain reliever? Show your calculations.

b. You discovered that an error was made in the calculation of the mean pain relief time for the new pain reliever. The mean pain relief time was X =7.1 with the same standard deviation (s = 3.5). Do your conclusions for question a change as a result of discovering this error? Show your calculations.

c. What is the p-value for the test statistic used in the hypothesis test in question b?