7. A femur fracture is a major burden among elderly people, leading patients to be bedridden for a long time in the hospital. A recent study was interested in whether carbohydrate loading before surgery would reduce the postoperative pain in the femurs of elderly patients. So they randomly sampled a treatment group who carbohydrate loaded before their surgery and a control group whom did not, with a sample size of 33 in each group. They measured postoperative pain using the Visual Analogue Score (VAS) and the treatment group had a mean VAS score of 4.8 with a standard deviation of 1.8 while the control group had a mean VAS score of 6.1 and a standard deviation of 2.1.

a) Perform a hypothesis test and give a 95% confidence interval for the difference in average VAS scores between the carbohydrate loading group and the control group. Assume the population standard deviation of each group is equivalent. Be sure to include all 8 steps of your hypothesis test and interpret your confidence interval.

b) The researcher concluded that the VAS scores were different between the two 2 groups, did your analyses in part (a) show evidence to agree with this conclusion?

c) Instead of performing a two sample confidence interval for the difference in average VAS scores between the two groups like I taught you to do in this course (and that you did in part (a)), the researchers chose to do two, one sample confidence intervals (one for each group) and determined that the VAS scores were different using only those two, one-sample confidence intervals (CI for treatment group: (4.7-5.4) and CI for control group: (5.3-6.8)). Ignoring that their method of performing and comparing two one-sample intervals is questionable statistics, based on their intervals provided, do you agree with their conclusion that VAS scores are significantly different between the groups?