Question

In a previous homework, you used the delta method to determine the approximate distribution of the estimated log-odds for large sample size, where the odds of success are defined as probability of success probability of failure Now suppose that Y~ Binomial(n,P),independent of YBinomial(n2 Pa), where both n and n odds in group p/(-p) are large. The odds ratio is defined as odds in group 2 Pa/(1 Pa) (a). Consider the log-odds ratio, pa/(1 P2) Construct an approximate (1-a) 100% confidence interval for the log-odds ratio. PI 1 -P2 (b). The British Medical Journal reported the following data for 114 patients with spondyloarthropathies (a kind of joint disease) and 334 patients without spondyloarthropathies. In the "with" group, 54 had the ABO secretor state (a genetic feature), and in the "without group, 89 had the ABO secretor state. The journal reported an odds ratio of 2.48 and a 95% confidence interval of 1.59 3.85 Use your computed confidence interval from 3(a) to reproduce the journal's reported confidence interval.

Answer 1

First I construct the confidence interval in general. The find 95% confidence interval for the given data.

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