Question # 8 [12 pts] Suppose two independent random samples were taken. The following data were recorded: Quebec: Rest of Canada: n = 150, n = 1000, Number of deaths due to cancer = x = 47 Number of deaths due to cancer = x2 = 291 Page 4 a) Suppose the scientists have no preconceived theory concerning which proportion parameter is the larger and they wish to detect only a difference between the two parameters, if it exists. What should they choose as the null and alternative hypotheses for a statistical test? b) What type of error could occur in testing the null hypothesis in (a), if Ho is false? c) Test the hypotheses in (a) by using an appropriate test statistic. Draw your conclusions. Use the significance level a = 0.01. d) Use a 99% confidence interval to estimate the actual difference between the cancer death proportions for the people in Quebec versus rest of Canada. Does your confidence interval estimate provide the same conclusion as in part (a)? Justify your answer.