A study would like to investigate the risk of lung cancer in url. area and rural area. Assume the proportion of urban residents with lung cancer is p1, and the proportion of rural area residents with lung cancer is p2. If it is found that 20 of 200 adults in an urban community have lung cancer and 10 of 150 adults in the rural community have lung cancer. Find the 95% confidence interval for the difference in the proportions. Would you conclude that p1 is greater than p2? Select all correct answers. "O" is not in the interval (C.I) O Yes, we can conclude p1 is greater than p2. "O.1" is in the interval (C.I) "O" is in the interval (C.I) Not enough information is given. O (-0.02431, 0.090972) O (21.48721, 22.90809) O No, we can't conclude p1 is greater than p2. "0.1" is not in the interval (C.I) O (-1.21908, 2.64790) O (-19.20998, -17.21458)

Answered: Image /qna-images/answer/e6bc6ab8-22a8-49f4-b9bf-84c0c61e6057.jpgDenote p1, p2 as the true population proportions risk of lung cancer in urban and rural area, respectively. It is needed to test, whether p1 is greater than p2. Null hypothesis: H0: p1 = p2. Alternative hypothesis: H1: p1 > p2. It is given that, among a random sample 200 adults 20 has risk of lung cancer in urban area. That is, x1 = 20 and n1 = 200. It is given that, among a random sample 150 adults 10 has risk of lung cancer in rural area. That is, x2 = 10 and n2 = 150. The sample proportions are: p̂1 ≈ 0.100 (= 20/200). p̂2 ≈ 0.067 (= 10/150). If 95% of the observations must lie within an interval, the remaining 5% must lie outside the interval. Further, due to symmetry, 2.5% will lie above the upper limit and the remaining 2.5% will lie below the lower limit of the interval. Thus, the upper limit of the interval is such that, 97.5% lie below it As a result, zα/2 = z0.025 ≈ 1.96 [Using Excel formula: =NORM.S.INV(0.975)]. Now, substitute the obtained values in the formula of confidence interval. Thus, the 95% confidence interval is –0.02431 < p1 – p2 < 0.090972. The confidence interval contains 0. Hence, it can be said that, there is not enough evidence to claim that, p1 is greater than p2. The correct options are: 1 in the interval (C.I.). 0 is in the interval (C.I.). (–0.02431,090972).\ No, we can’t conclude p1 is greater than p2.