1. A study of patients with insulin-dependent diabetes was conducted to investigate the effects of cigarette smoking on renal and retinal complications. Before examining the results of the study, you wish to compare the baseline measures of systolic blood pressure across four different subgroups: nonsmokers, current smokers, ex-smokers, and tobacco chewers. A sample is selected from each subgroup; the relevant data are shown below. Means and standard deviations are expressed in mm Hg. Assume that systolic pressure is normally distributed.
standard deviation Nonsmokers 269 115 13.4 Current Smokers 53 114 10.1 Ex-smokers 28 118 11.6 Tobacco Chewers 9 126 12.2
(a) Calculate the estimate of the within-groups variance. (b) Calculate the estimate of the between-groups variance. (c) At the 0.05 level significance, test the null hypothesis that the mean systolic blood pressures of the four groups are identical. What do you conclude? (d) If you find that the population means are not equal, one approach to doing multiple comparisons is the Bonferroni procedure. What would the significance level of each individual test be if this method were used?
2. The data set lowbwt contains information for a sample of 100 low birth weight infants born in two teaching hospitals in Boston. Systolic blood pressure measurements are saved under the variable name sbp and gender under the name sex.
(a) Assuming equal variances for males and females, use the two-sample t-test to evaluate the null hypothesis that among low birth weight infants, the mean systolic blood pressure for girls is identical to that for boys. (b) Even though there are only two populations instead of three or more, test the same null hypothesis using the one-way analysis of variance. (c) In the book, the statement has been made that in the case of two independent samples, the F-test used in the one-way analysis of variance reduces to the twosample t-test. Do you believe this to be true? Explain briefly.