With this table of data, (a) Construct a 95\\% confidence interval for the diffe

Question

With this table of data,

(a) Construct a 95% confidence interval for the difference in the true proportion of having lung cancer among smokers (pi_S) and true proportion of having lung cancer among non-smokers (pi_N). Interpret your result.

(b) Is smoking related to lung cancer? Test the appropriate hypothesis at the 5% significance level.

Construct a 95% confidence interval for the difference in the true proportion of having lung cancer among smokers (pi_S) and true proportion of having lung cancer among non-smokers (pi_N). Interpret your result. Is smoking related to lung cancer? Test the appropriate hypothesis at the 5% significance level.

Explanation / Answer

(a) p1=688/709 =0.9703808

p2=21/709 =0.02961918

Given a=0.05, Z(0.025) =1.96 (from standard normal table)

So 95% confidece interval is

p1-p2 +/- Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

--> (0.9703808-0.02961918)+/- 1.96*sqrt(0.9703808*(1-0.9703808)/709+0.02961918*(1-0.02961918)/709)

--> (0.9231132, 0.95841)

We have 95% confident that the population proportion difference will be within this interval.

(d) Ho: smoking is not related to lung cancer

Ha: somking is related to lung cancer

Yes   No   Total   Yes Observed   688 650 1338
Expected   669.00 669.00 1338.00
(O - E)

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