In the ﬁrst study, the investigators separately sampled CHD cases and controls and interviewed them to ﬁnd out if they had been following this new diet.In the second study, subjects were recruited from the same target population and randomly assigned to follow the new diet or not; the occurrence of CHD was then measured. The ﬁrst study reports a pooled odds ratio estimate of 2.3 (95% conﬁdence interval:2.0 -2.7); the second study reports a pooled odds ratio estimate of 3.5 (95% conﬁdence interval:3.1 – 3.9).The investigators in the ﬁrst study also recorded whether subjects had been physically active or not.Among physically active subjects, they found an odds ratio of 0.5 (95% conﬁdence interval:0.2 – 0.7);among inactive subjects, they found an odds ratio of 2.1 (95% conﬁdence interval:1.4 – 2.9).Assumethat CHD incidence is measured over a fairly short time period so that the disease can be consideredrare. Based on these data, brieﬂy discuss whether the following statements are likely to be true or false. (a)The new diet and the risk for CHD are independent of each other in the target population. (b)The relationship between the diet and risk for CHD is confounded in the ﬁrst study. (c) The χ2 test for homogeneity across physical activity levels is likely to yield a p-value smaller than 0.05 in the ﬁrst study (d)The Cochran-Mantel-Haenszel test has high power for detecting an association between the dietand CHD after controlling for physical activity in the ﬁrst study.