3) A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear, known as middle-ear effusion. The presence of fluid may result in temporary hearing loss and interfere with normal learning skills in the first 2 years of life. One hypothesis is that babies who are breast fed for at least one month build up immunity against the effects of the disease and have less prolonged effusion than formula fed babies. A small study of 24 pairs of babies is set up, where babies are matched on a one-to one basis according to age, sex, socio-economic status, length of gestation, and medications used. One member of each matched pair is a breast-fed baby whereas the other member is a formula fed baby. The outcome variable is the duration of middle ear effusion after the first episode of otitis media.

3) Continued

1. If the data is assumed to be normally distributed, what is the appropriate test? Perform that test using =. 05.
2. If the data are assumed not to be normally distributed, one appropriate nonparametric test that can be applied is the sign test. Perform this test using =. 05.
3. Which of these tests do you believe to be the most appropriate for the data? Justify your answer.

4) Researchers have always been interested in the neuromodulation of immune function. Irwin and colleagues (1987) published results of a study that investigated the relationship between stressful major life events and immune function. Subjects in the study were women who husbands were undergoing treatment for metastatic lung cancer, women whose husbands had died of lung cancer 1 to 6 months prior to the study, and women whose husbands were in good health. Scores on the Social Readjustment Rating Scale (SRRS) were recorded for each woman. According to their scores on the Social Readjustment Scale, the women were divided into three groups: those with low scores (≤ 54), those with moderate scores (55-99), and those with high scores (≥ 100). The researchers want to determine whether the mean level of natural killer cell activity differs between the groups.

1. State the null and alternative hypotheses. What assumptions are necessary to perform this test?
2. Perform the appropriate statistical test using =. 05 and check the assumptions. Provide all outputs required to check assumption.
3. Perform pairwise comparisons of the groups means using the Bonferroni method.
4. Are you confident the assumptions hold? Explain. In light of your opinion, interpret the results.
5. The output below is from an appropriate non-parametric test to test whether the median cell activity levels differ? Do these results strengthen or weaken you convictions about the conclusion you drew in part d)? Explain.

1. Suppose a clinical trial is conducted to test the efficacy of a new drug, spectinomycin, in the treatment of gonorrhea for females. Forty-six patients are given a 4 grams daily dose of the drug and seen one week later, at which time six of the patients still have gonorrhea.

1. What is the best point estimate of p, the probability of a failure with the drug? What is the standard error of the estimate?
2. What is a 95% confidence interval for p?
3. Suppose we know that penicillin G at a daily dose of 4.8 mega-units has 10% failure rate. Conduct the appropriate test to determine if the rate of failure for spectinomycin differs from 10%.
4. What role does the central limit theorem play in this problem?

1. The SF36 is a psychometric scale that measures quality of life. A random sample of 20 male first semester graduate students and a random sample of 20 female first semester graduate students were taken to determine if the mean scores for quality of life differed between genders. The data are presented below.

1. If the data is assumed to be normally distributed, what is the appropriate test? Perform that test using =. 05.
2. If the data are assumed not to be normally distributed, one appropriate nonparametric test that can be applied is the sign test. Perform this test using =. 05.
3. Which of these tests do you believe to be the most appropriate for the data? Justify your answer.
4. What role does the central limit theorem plat in your answer to c? Explain.

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