1. You are interested in whether the data you have collected provide sufficient evidence to indicate a difference in mean serum uric acid levels between individuals without Down’s syndrome and individuals with Down’s syndrome. The data consist of serum uric acid readings on 12 individuals with Down’s syndrome and 15 individuals without Down’s syndrome. The means are 4.5 mg/100 ml for the Down’s sample and 3.4 mg/100 ml for the sample of individuals without Down’s syndrome. Assume that the two independent samples are drawn from normally distributed populations with variances equal to 1 and 1.5 for the Down’s and non-Down’s samples, respectively. Do you have sufficient evidence to indicate a difference in uric acid levels? Assume α = 0.05, state the hypothesis that you are testing, show all calculations, provide the p value for the test statistic, and provide the 95% confidence interval for the difference between the two means.
2. You are interested in the familial aggregation of cholesterol levels. Suppose cholesterol levels are assessed in 100 children, 2 to 14 years of age, of men who have died of heart disease and it is found that the mean cholesterol level in the group is 207.3 mg/dL with a standard deviation of 35.6 mg/dL. Data from 74 controls were also collected for children in the same age range with fathers that are alive and do not have heart disease, and the results for this sample were a mean cholesterol level of 193.4 mg/dL with a standard deviation of 17.3 mg/dL. You know that both populations from which the samples were taken are normally distributed, and while you do not know the population variances you believe that they are unequal in the two populations. Can you conclude that the cholesterol levels in the two groups differ? Assume α = 0.05.