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 8
Due Date: Friday, Dec. 07, 2007

Please, submit your homework right after lecture on the due date. See the HW submission rules. On the front page include the following header.
• (HW_8
• Do these problems on pages 316-386 from Samuels & Witmer's text Statistics for the Life Sciences, Prentice Hall (2003).
• 8.4: In a study of 1,040 subjects researchers found that the prevalence of coronary heart disease increased as the number of cups of coffee consumed per day increased:
• What is the explanatory variable?
• What is the response variable?
• What are the observational units?
• 8.9: Olestra is a no-calorie, no-fat additive that is used in the production of some potato chips. After the US FDA approved the use of olestra some consumers complained of Olestra induced stomach cramps and diarrhea. A randomized double-blinded experiment was conducted in which some participants were given bags of chips made with olestra and others were given ordinary potato chips. In the olestra group, 38 % of the subjects reported having gastrointestinal symptoms. In the group eating the regular chips that number was 37%. (The two percentages are not statistically significantly different). Explain how the placebo effect/no-placebo effect is related in this experiment. Also, explain why was it important to do this as a double-blinded study.
• 8.20: In a pharmacological experiment on eating behavior in rats, 18 rats are to be randomly allocated to 3 treatments (T1, T2 and T3). During the experiment, the animals are kept in cages in a rack. The rack has 3 tears with 6 cages per tear. Lighting conditions varied somewhat between different tiers (bottom rack is darkest). It's known that lighting conditions correlate with eating behavior in rats. Rank (best to worst) these three plans proposed for allocation of the rats to cages. Explain your choices.
• Plan I: Randomly allocate the 18 rats to the 18 cages
• Plan II:  Put the T1 rats in tier 1, T2 rats in tier 2 and T3 rats in T3.
• Plan III: On each tier put 2 rats from each of the 3 treatments.
• 8.29: SUppose someone conducts a randomized response sample, as explained in example 8.28, and find that 43 out of 104 people answered "Yes". What is the resulting estimate of p. the population percentage for whom the truthful answer to the sensitive question is "Yes"?
• 9.3: Cyclic adenosine monophosphate (cAMP) can mediate cellular response to hormones. In a study of maturation of egg cells in the frog Xenopus laevis, oocytes from each of four females were divided into 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.

 cAMP (pmol/oocyte) Frog Control Progesterone d 1 6.01 5.23 0.78 2 2.28 1.21 1.07 3 1.51 1.40 0.11 4 2.12 1.38 0.74 Mean 2.98 2.31 0.68 SD 2.05 1.95 0.40

1. Calculate the standard error of the mean difference between the varieties.
2. Calculate the 95% CI for the mean difference μ1 − μ2.
3. Test Ho : μ1 = μ2 = 0 at a = 0.05 using a paired t-test.
• 9.19: Twenty institutionalized epileptic patients participated in a study of a new anticonvulsant drug, Valproate. Ten of the patients (chosen at random)
were started on the daily Valproate and the other ten received an identical placebo pill. During an eight-week observation period, the number of major and minor seizures were counted. After this, the patients were “crossed over” to the other treatment, and seizure counts were made during a second eight week observation period. We would use the independent / dependent (paired) samples method in order to conduct a test of hypothesis. (Note that this analysis ignores the possible effect of time, that is, first vs. second observation period).
 Patient Number Placebo Period Valproate Period 1 37 5 2 52 22 3 63 41 4 2 4 5 25 32 6 29 20 7 15 10 8 52 25 9 19 17 10 12 14 11 7 8 12 9 8 13 65 30 14 52 22 15 6 11 16 17 1 17 54 31 18 27 15 19 36 13 20 5 5
• 9.33: In an investigation of possible brain damage due to alcoholism, an X-ray procedure known as a computerized tomography (CT) scan was used to measure brain densities in eleven chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, education, and other factors. The brain density measurements on the alcoholics and the matched controls are reported in the accompanying table. Use an appropriate statistical test (justify your choice) to assess a null hypothesis of no difference against the alternative that alcoholism reduces brain density at a=0.02.
 Pair Alcoholic Control Difference 1 40.1 41.3 -1.2 2 38.5 40.2 -1.7 3 36.9 37.4 -0.5 4 41.4 46.1 -4.7 5 40.6 43.9 -3.3 6 42.3 41.9 .4 7 37.2 39.9 -2.7 8 38.6 40.4 -1.8 9 38.5 38.6 -0.1 10 38.4 38.1 .3 11 38.1 39.5 -1.4 Mean 39.14 40.66 -1.52 SD 1.72 2.56 1.58
• Practice problems (Do not turn in):  10.4, 10.5, 10.6, 10.11, 10.17, 10.22, 10.35, 10.37, 10.73, 10.87, 10.96 - pages 400-461, Samuels & Witmer's text Statistics for the Life Sciences, Prentice Hall (2003).

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