Data from two processes is provided in the accompanying file. The values collected represent a specific immune response; the higher the number, the better the immune system is functioning. One question researchers naturally want to know is whether the intervention is having a positive effect, and, in this case, if one process is more effective than the other. TASKS a) Calculate summary measures using appropriate unbiased point estimates for the mean and standard deviation for each data set. b) Create appropriate frequency histograms for each data set and comment upon what these suggest about each data set. c) Create and interpret normal probability plots (ala Fig 6-23 of the text) for each data set. Clearly document the cumulative frequency adjustment factor used, explaining what led you to that factor. d) Create 99% two-sided confidence intervals for the population means and variances. (Not differences in those values, but independent intervals.) Provide a practical interpretation of these intervals. e) Discuss what would happen to the intervals of d) and why it happens if the summary measures that you found in part a) were found with sample sizes of 10 instead of the much larger numbers that that they are. It is okay to actually calculate the intervals, but be sure to explain why the intervals change or remain the same. That explanation should not be, for example, the interval stayed the same because the multiplier used was the same. Rather, if such an item did stay the same, explain why it did using the underlying concepts of the course. f) Conduct a test regarding the equivalence of the means at the 0.05 level of significance. Clearly indicate assumptions made regarding variance and what, if anything, suggests that the assumptions are reasonable. g) Determine the power of the test conducted in part f) if the delta difference in the means is 10. h) Repeat the test of part f) assuming that the summary measures of part a) were found with sample sizes of 10 instead of the much larger numbers that they are. i) Conduct a test regarding the equivalence of the variances at the 0.05 level of significance. Clearly indicate assumption and your rationale for choosing either a one or two-sided test. j) Discuss what the results of parts a) through i) suggest about whether one process is more effective than the other from a statistical perspective.

Process 1 :

9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 31, 31, 31, 31, 32, 32, 34, 34, 34, 34, 34, 35, 35, 36, 36, 36, 36, 38, 38, 39

Process 2 :

18, 19, 19, 20, 20, 21, 22, 22, 22, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 34, 35, 35, 36, 36, 36, 37, 37, 37, 37, 38, 38, 38, 38, 39, 39, 41, 45, 47