Question 7 (12 marks) A random sample of 180 men of a certain country indicated that 50 were smokers, and of 150 women Inst surveyed 30 indicated that they smoked. Let pm and pw denote the proportions of men and women, respectively. in the country who smoke. a. Check the conditions required for in e. (2 marks) b. Do the data provide sufficient evidenceanat the proportion of men who smoke is higher than the proportion of women who smoke? Carry out the appropriate test using a = 0.05; state the hypotheses, give the test statistic value, the p-value, and state your conclusion. (5 marks) c. Create a 90% confidence interval for Pm - Pw. (4 marks) d. Based on your interval (in C), is there a difference between the proportions of men and women who smoke? Explain. (1 mark)