Stat 538: Biostatistics I Homework 6, due Thursday Oct. 20 in lab 1. Cyclic adenosine monophosphate (cAMP) is a substance that can mediate cellular response to hormones. In a study of maturation of egg cells in the frog Xenopts laevis, oocytes from each of four females were divided into two batches: one batch was exposed to progesterone and the other was not. After two minutes, each batch was assayed for its cAMP content, with the results given in the table below. cAMP (pmol/oocyte) Frog Control Progesterone 1 6.01 5.23 2 2.28 1.21 3 1.51 1.40 4 2.12 1.38 Use Minitab for this problem. a. Explain why this is a paired design. b. Make a dotplot and box plot of the differences between the cAMP levels for the control and progesterone samples. c. Test at the 5% level whether there is any difference in the population mean cAMP levels for batches of oocytes that are untreated versus those treated with progesterone. d. Obtain and interpret a 95% CI for the difference in population mean cAMP levels for batches of oocytes that are untreated versus those treated with progesterone. e. Discuss any statistical assumptions that you have made in carrying out the analysis, and whether the assumptions seem reasonable. f. Write a short summary to the problem. 2. These data were used in HW 3 (and appear again below). Do all the calculations in Minitab. The following data were collected from 48 women who were at least 40 years old when they gave birth to their first child. The data concern the gestation period of that pregnancy, and related variables on the child and mother. The columns are, from left to right: 1) ID 2) The child's gestation period, in weeks 3) Sex of the child (0=Male, 1=Female) 4) Birth Weight of child, in grams 5) Number of cigarettes smoked per day (on average) by the mother 6) Height of mother in cm 7) Weight of mother in kilograms at first prenatal visit 8) Weight of mother in kilograms at final prenatal visit For these data, we are interested in comparing the distribution of birth weights for males to females. a. Using Minitab, describe the shapes, and make sure to compare the centers and spreads for the birth weights of males and females. Do the distributions appear to be reasonably normal with similar spreads? Does there appear to be much of a difference in the typical birth weights for males compared to females? Discuss briefly. b. Do a formal test at the 5% level that the population mean birth weights are the same for males and females. Use the pooled t-test and do the test by comparing the p-value to .05. Also, compare the result with what you get from the Satterthwaite (Welch) test. c. Construct and interpret a 95% CI for the difference in population mean birth weights between males and females. d. Write a short summary of your analysis. Include any problems with assumptions you might see that could affect the validity of your conclusions. Extra Credit: Repeat parts b and c using the Mann-Whitney test. Would you change any conclusions using that analysis? DATA ---- 01 36 0 3300 0 160.0 67.3 82.7 02 38 0 3300 60 167.6 52.7 76.0 03 38 0 4100 20 167.6 64.2 79.6 04 38 1 2900 10 163.9 72.7 95.8 05 39 0 2820 0 161.3 50.0 63.3 06 39 0 3040 0 158.8 49.1 61.5 07 39 0 4120 0 160.0 57.7 73.5 08 39 0 4200 0 174.0 68.0 86.8 09 39 1 3100 0 171.5 67.3 85.6 10 39 1 3330 0 160.0 74.0 90.5 11 39 1 3410 0 165.1 55.9 70.7 12 39 1 3420 0 162.6 52.3 66.0 13 40 0 2450 20 167.6 61.4 72.5 14 40 0 2885 0 167.7 60.0 78.6 15 40 0 3235 0 170.2 50.0 65.5 16 40 0 3320 0 165.1 63.6 80.2 17 40 0 3600 0 165.1 53.2 68.7 18 40 0 3720 0 165.0 57.7 74.4 19 40 0 3720 0 172.7 61.4 80.0 20 40 0 3820 0 175.3 60.8 78.1 21 40 0 3840 0 167.0 60.5 83.9 22 40 0 3880 0 156.2 57.3 73.7 23 40 0 3960 0 157.5 52.7 68.2 24 40 0 4465 0 157.5 51.4 66.4 25 40 1 2980 0 160.0 47.7 55.2 26 40 1 3040 0 162.0 49.0 60.3 27 40 1 3060 20 157.5 61.0 75.0 28 40 1 3100 0 170.2 55.5 64.6 29 40 1 3120 0 160.3 56.8 75.4 30 40 1 3205 0 172.7 58.2 75.5 31 40 1 3220 0 170.0 64.6 86.0 32 40 1 4100 40 167.0 67.0 85.0 33 41 0 3100 0 168.9 61.4 69.2 34 41 0 3720 0 170.2 57.7 67.7 35 41 0 3720 20 170.2 57.7 80.5 36 41 0 3900 0 167.0 68.0 85.4 37 41 0 3990 0 165.1 52.3 71.2 38 41 0 4050 0 167.6 61.0 78.5 39 41 0 4080 0 162.6 59.1 83.1 40 41 0 4100 0 165.1 60.5 86.5 41 41 0 4460 20 165.1 56.8 88.0 42 41 0 5220 0 157.5 56.8 68.2 43 41 1 3300 40 162.6 74.1 89.7 44 41 1 3400 0 172.7 71.4 87.8 45 41 1 4000 0 165.1 90.0 100.8 46 41 1 4030 0 166.0 63.0 95.3 47 43 1 3220 0 166.4 60.9 72.0 48 43 1 4270 0 162.6 54.5 70.3