Ivo Dinov
UCLA Statistics, Neurology, LONI

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STAT 13

Introduction to Statistical Methods for the Life and Health Science

Department of Statistics

## Instructor: Ivo Dinov

Homework 6
Due Date: Friday, Nov. 21, 2008

Please, submit your homework before lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW_6) Do the following problems:
• In a study of the development of the thymus gland, researchers weighted the glands of 10 chick embryos. Five of the embryos had been incubated for 14 days and five had been incubated for 15 days. The weights of the thymus glands are reported below.
• Use the T test to compare the means at a = 0.10.
• Not that the chicks that were incubated longer had smaller mean thymus gland. Explain this backwards result!
• Compare  your results agains the SOCR T-test Analysis applet.
 Index Thymus Grand Weight 14 days Thymus Grand Weight 15 days 1 29.6 32.7 2 21.5 40.3 3 28 23.7 4 34.6 25.2 5 44.9 24.2 n 5 5 y- 31.72 29.22 S 8.73 7.19
• The table below contains the number of bacteria colonies present in each of several petri dishes after E. Coli bacteria were added to the dishes and they were incubated for 24 hours. The "soap" dishes contained a solution prepared from ordinary "soap" the "control" dishes contained a solution of sterile water.
• Use the T-test to investigate soap affects on the number of bacteria colonies that form (use a = 0.10).
• State your conclusions in the context of the study.
• Compare  your results agains the SOCR T-test Analysis applet.

 Index Control Soap 1 30 76 2 36 27 3 66 16 4 21 30 5 63 26 6 38 46 7 35 6 8 45 n 8 7 y- 41.8 32.4 S 15.6 22.8 SE 5.5 8.6
• Ferulic acid is a compound that may play a role in disease resistance in corn. A botanist measured the concentration of soluble ferulic acid in corn seedlings grown either in the dark or in a light/dark photo period. The results (nmol acid per g of tissue) are shown in the table.
• What is a reasonable scientific question to ask for this study and that is the critical population parameter of interest?
• Construct a 92% CI(parameter)
• Construct a 82% CI (Parameter)
 Sample Mean Sample Standard Deviation Sample Size Dark 92 13 4 Photo period 115 13 4

• In a field study of mating behavior in the Mormon cricket (Anabrus simplex), a biologist noted that some females mated successfully while others were rejected by the males before coupling was complete. The question arose whether some aspect of body size might play a role in mating success. The data below summarizes measurements of head width (mm) in the two groups of females.
• Construct a 95% confidence interval for the difference in population means
• Interpret your CI in the context of the study.
 Successful: n=22 mean=8.500 S=0.289 Unsuccessful: n=17 mean=8.441 S=0.262

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