An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe, but the new method has the potential to reduce operating time. Five surgeons each operate on two patients that have been matched by age, sex, and other relevant factors, performing the old procedure on one patient and the new procedure on the other. The time to complete each surgery (in minutes) is recorded in the following table.
Surgeon 1 Surgeon 2 Surgeon 3 Surgeon 4 Surgeon 5
Old Way 36 55 28 40 62
New Way 29 42 30 32 56
(a) Conduct a hypothesis test at signi_cance level _ = 0:05 to decide if there is enough evidence to conclude that the new procedure is faster than the old one.
You can assume that the di_erences between the old and new times are normally distributed. As always, clearly state your hypotheses, the observed value of the appropriate test statistic, the number of degrees of freedom of the test statistic you are using, the p-value (or bounds on the p-value) that you will base your conclusion on, and state your actual conclusion.
(b) Use Excel to conduct the same hypothesis test as you conducted in part (a): To do this you will need to first enter the times for each method into two columns of a spreadsheet. Then, under the Data menu, and under the Data Analysis Tools menu, select the paired t-test. You will need to enter the Variable 1 Range and the Variable 2 Range. I used (A1:A5) and (B1:B5). Then enter the value of the Hypothesized Mean Difference as 0 and specify the value for first which the test is being conducted. Cut and paste the output of the test into a word-processing document and include it with your assignment. You may need to stretch the columns of the output so that you can read all of the entries in the cells.
Under your table, clearly state the observed value of the test statistic and the p-value given by Excel. Note that Excel will provide two p-values, depending on whether the test is a two-tailed test or a one-tailed test. Select the appropriate one. Would you make the same conclusion that you made in part (a)?