3. [12 marks] Consider a hypothetical case-control study to examine the relationship between smoking and ovarian cancer among nulliparous women. The data from this study are given in Table 1 stratified by the use of oral contraceptives. (a) [2 mark] Estimate the crude (unadjusted) Odds Ratio for the association between smoking and ovarian cancer. (b) [4 marks] Use the formal definition of confounding to determine if the use of oral contraceptives is a potential confounder for the relationship between smoking and ovarian cancer. Support your claims with specific odds ratio estimates and suitable statistical hypothesis tests. (c) [3 marks] Use the Mantel-Haenszel method to calculate a pooled Odds Ratio. Give a one sentence interpretation of your estimate. (d) [3 marks] Use the Mantel-Haenszel test to determine whether the Odds Ratio calcu- lation in (c) is statistically significant. Be sure to clearly state the null and alternative hypotheses, give the formula for the test statistic, calculate its value, and find the p-value. What is the conclusion of the test? Table 1: Hypothetical case-control study on smoking and ovarian cancer Never-users of oral contraceptives Ever-users of oral contraceptives Smoking Total Smoking Total Yes No Yes No Ovarian cancer cases 9 32 41 15 4 19 Controls 8 28 36 50 12 62 Total 17 60 77 65 16 81