Question

Please read the question carefully. Problem: Proportion of ”Cured” Cancer Patients: How Does Canada Compare with...

Problem: Proportion of ”Cured” Cancer Patients: How Does Canada Compare with Europe? Lung cancer remains the leading cause of cancer death for both Canadian men and women, responsible for the most potential years of life lost to cancer. Lung cancer alone accounts for 28% of all cancer deaths in Canada (32%. in Quebec). Most forms of lung cancer start insidiously and produce no apparent symptoms until they are too far advanced. Consequently, the chances of being cured of lung cancer are not very promising, with the five-year survival rate being less than 15%. The overall data for Europe show that the number of patients who are considered ”cured” is rising steadily. For lung cancer, this proportion rose from 6% to 8%. However, there was a wide variation in the proportion of patients cured in individual European countries. For instance, the study shows that for lung cancer, less than 5% of patients were cured in Denmark, the Czech Republic, and Poland, whereas more than 10% of patients were cured in Spain.

1. Suppose a sample of 75 Quebecers was selected and it was found that 27 of them had died due to lung cancer.

(a) Perform the appropriate test of hypothesis to determine whether the proportion of deaths in Quebec due to the leading cause (lung cancer) has changed. Test using α = 0.05. (b) Find the p-value for this test and interpret it.

(c) Construct a 95% confidence interval estimate of the population proportion of the premature cancer death in Quebec.

(d) Explain how to use this confidence interval to test the hypotheses.

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