Example 1 and 2

Two Sample Proportions - Inference Examples Example 1: The November 20, 1992 issue of The Harrisburg Evening-News reported the failure rates for coronary artery bypass surgery in Pennsylvania in 1990. The newspaper reported the number of patients who underwent the operation and the number who died during or after surgery, broken down by geographic region, by hospital, and by physician. Central Pennsylvania had 125 deaths in 3676 operations, compared to 288 deaths in 6313 operations for the southeastern region. a) Assess whether the recovery rates differ significantly between the two regions. Use significance level of 0.05. b) Give an 80 percent confidence interval for the difference between the recovery rates in the two regions.Example 2: A newspaper account of a medical study claimed that the daughters of women who smoked during pregnancy are more likely to smoke themselves. The study surveyed children asking them if they had smoked in the last year and then asked the mother if she had smoked during pregnancy. Only 4% of the daughters of mothers who did not smoke during pregnancy had smoked in the past year, compared to 26% of girls whose mothers had smoked during pregnancy. a) Suppose there had been 50 girls in each group. Is there evidence to support the claim? Use a significance level of 0.01. b) Construct a 98% confidence interval for the difference in the smoking rates of girls whose mothers smoked and those whose mothers did not