Rauch et. al. (2012) compare Small Bowel Transit time in critical care patients and in healthy patients by testing for a difference in medians (table 2). The following table provides summary statistics for the SBtime based on whether or not patients were in critical care or were healthy. Use the following information to conduct the following hypothesis test for a difference in means, and compare it to the authors' test for a difference in medians:

-A two-tail T-test for a two-sample difference in means at the 95% confidence level

-with Null Hypothesis that the average SBtime in critical care patients is equal to the average SBtime in healthy patients.

-and with Alternate Hypothesis that the average SBtime in critical care patients is not equal to the average SBtime in healthy patients

1.Calculate the sample mean, sample standard deviation, and sample size for each group. Calculate and interpret the mean difference and the ratio of the means. (10%)

2.Calculate the test statistic using the Satterwaithe method, (10%)

3.Calculate and interpret the p-value of the test, P(|T| > |T_test|). (10%)

4.Compute and interpret a confidence interval for the difference in the average SBtime in critical care patients compared to healthy patients. (10%)

5.Summarize the results of the hypothesis test. Explain your decisions and Justify your claims. (15%)