A study looked at the relationship between coronary heart disease (CHD) and coffee consumption in a group of 40-55 year old men. Among the 790 heavy coffee drinkers (at least 100 cups per month), there were 38 CHD cases. Among the 928 moderate and non-drinkers (less than 100 cups per month), there were 39 CHD cases.

(a) Test the hypothesis that the rate of CHD is higher for heavy coffee drinkers at the 5% level of significance.

(b) Obtain the p-value for the value of the test statistic in (b).

(c) What would the p-value be if the hypothesis to be tested was simply that the rate of CHD differs between the two groups?

(d) Obtain a 95% confidence interval for the difference in the population proportions of CHD cases between the two categories of coffee drinkers.