1 The following data come from a study designed to investigate drinkin problems among college students. In 1983, a group of students were asked whether they had ever driven an automobile while drinking. In 1987, after the legal drinking age was raised, a different group of college students were asked the same question.
Year
Drove While Drinking 1983 1987 Total
Yes 1250 991 2241
No 1387 1666 3053
Total 2637 2657 5294
a.) Use the chi-square test to evaluate the null hypothesis that the population proportions of students who drove while drinking are the same in the two calendar years.
b.) What do you conclude about the behavior of college students?
c.) Again test the null hypothesis that the proportions of students who drove while drinking are identical for the two calendar years. This time, use the method based on the normal approximation to the binomial distribution that was presented in Section 14.6 (comparisons of two porportions-stata) Do you reach the same conclusion?
d.) Construct a 95% confidence interval for the true difference in population proportions.
e.) Does the 95% confidence interval contain the value 0? Would you have expected that it would?
2.A group of children five years of age and younger who were free of respiratory problems were enrolled in a cohort study examining the relationship between parental smoking and the subsequent development of asthma. The association between maternal cigarette smoking status and a diagnosis of asthma before the age of twelve was examined separately for boys and for girls.
Gender Smoking Status Asthma Diagnosis Total
Yes No
Boys> ½ pack/day 17 63 80
< ½ pack/day 41 274 315
Total 58 337 395
Girls > ½ pack/day 8 55 63
< ½ pack/day 20 261 281
Total 28 316 344
a.) Estimate the relative odds of developing asthma for boys whose mothers smoke at least one-half pack of cigarettes per day versus those whose mothers smoke less than this.
b.) Estimate the corresponding odds ratio for girls.
c.) Conduct a test of homogeneity to determine whether it is appropriate to combine the information in the two 2x2 tables using the Mantel-Haenszel method. What do you conclude?
d.) If it makes sense to do so, find a point estimate for the summary odds ratio and construct a 95% confidence interval.
e.) What would you do if the results of the test of homogeneity led you to reject the null hypothesis that the odds ratio is identical for boys and girls?