The following table provides summary statistics for theDurationSurgery based on whether or not patients contracted an SSIfrom the Seasonal Effect data set. One of the researchers iscurious whether there is evidence to suggest that surgery durationwas longer in patients who contracted SSIs. Use the followinginformation to conduct the following hypothesis test:

• A one-tail T-test for a two-sample difference in means at the99% confidence level
• with Null Hypothesis that the average surgery duration inpatients that did contract SSIs is equal to the average surgeryduration in patients that did not contract SSIs
• and with Alternate Hypothesis that the average surgery durationin patients that did contract SSIs is greater than the averagesurgery duration in patients that did not contract SSIs

Seasonal Effect	Duration of Surgery
	Average	St. Dev.	Count
No SSI	3.506	1.899	2678
Yes SSI	4.418	2.243	241

a. Calculate the standard error of the mean for each group.(10%)

b. Using the correct degrees of freedom (df = group X size +group Y size ? # of groups), the correct number of tails, and atthe correct confidence level, determine the critical value oft. (10%)

c. Explain under which scenarios using a pooled variance beinadvisable, then, calculate the pooled variance (formula forS² is onpage 379) for the groups. (10%)

d. Calculate the test statistic, T_test (formula fort is on page 380). (10%)

e. The sleep center’s statistician tells you that the p-valuefor the test is less than 0.0001. Summarize the result of thestudy. Compare the mean scores in each group. Compare the teststatistic to the critical value. Compare the p-value to alpha. Doyou find a statistically significant difference? Is there ameaningful/practical difference? Explain your decisions and Justifyyour claims. (15%)