Question

The proportion of deaths due to lung cancer in males ages 15-64 in England and Wales during the period 1970- 1972 was 12%. Suppose that of 20 deaths that occur among male workers in this age group who have worked for at least 1 year in a chemical plant, 5 are due to lung cancer. We wish to determine whether there is a difference between the proportion of deaths from lung cancer in this plant and the proportion in the general population. 7.30 State the hypotheses to use in answering this question. 7.31 Is a one-sided or two-sided test appropriate here? 7.32 Perform the hypothesis test, and report a p-value. After reviewing the results from one plant, the company decides to expand its study to include results from three additional plants. It finds that of 90 deaths occurring among 15- to 64-year-old male workers who have worked for a least 1 year in these four plants, 19 are due to lung cancer 7.33 Answer Problem 7.32 using the data from four plants, and report a p-value. One criticism of studies of this type is that they are biased by the "healthy worker" effect. That is, workers in general are healthier than the general population, particularly regarding cardiovascular endpoints, which makes the proportion of deaths from noncardiovascular causes seem abnormally high 7.34 If the proportion of deaths from ischemic heart dis- ease (HD) is 40% for all 1 5-to 64-year-old men in England and Wales, whereas 18 of the preceding 90 deaths are attributed to IHD, then answer Problem 7.33 if deaths caused by IHD are excluded from the total.

Answer 1

7.30 The null and alternative hypotheses are: Ho: p 0.12 Hi. p # 0.12 7.31 This is a two-sided test 7.32 The formula and calculation of the test statistic is po (1-po) 7n 0.12 =-20 0.12(1-0.12 20 1.789 The calculation of p-value in Excel is NORMSDIST(1.789) 0.9632 Since the p-value is greater than the level of significance if considered 0.05, do not reject the null hypothesis and conclude that there is not enough difference between the proportion of death from lung cancer in the given plant and the proportion in the general population.

7.33 The formula and calculation of the test statistic is Po (1-Po) 19 0.12 0.12 (1-0.12) 90 -90 - 2.660 The calculation of p-value in Excel is: NORMSDIST 2.66) 0.9961 Since the p-value is greater than the level of significance if considered 0.05, do not reject the null hypothesis and conclude that there is not enough difference between the proportion of death from lung cancer in the given plant and the proportion in the general population.