For each of the following prompts, on a separate piece of paper, clearly (1) Identify the statistical test to use (by letter), {2) state the hypotheses of interest, (3) completely definite the parameters in the context of the problem, and (4) identify the degrees of freedom, if appropriate. The possible tests are listed in the table below; tests can be used more than once. (A) One sample mean Ztest (B) One sample ttest (C) Matched pairs ttest (D) Two-sample t-test (E) One-proportion Z-test (F) Two-proportion Z-test (G) Chisquare test (H) Regression (I) ANOVA (a) We hear that men are more likely to die from lung cancer than women. An SRS of 7,933 deaths due to lung cancer was taken and among them, 4,464 were men. Is there evidence that the majority of those who die from lung cancer are men? (b) A researcher wants to see if hair color {a proxy for skin complexion) makes one more susceptible to poison oak. Three hundred Caucasian volunteers are exposed to a small amount of poison oak. Their hair color (black, brown, blonde, red) and their susceptibility to poison oak {rash or no rash) are recorded. (c) A questionnaire measures an index of risk-taking behaviors in children. Scores are standardized so that 100 represents the population average, with children who take more risks than the typical child receiving scores greater than 100. The questionnaire was given to 10 boys and 10 girls. Is there evidence to support a claim that boys take more risks, on average, than girls? (d) Using church records, data from 1640 to 1870 recorded the number of sons that a woman had and her life length, for a total of 365 women. Does having a larger number of sons increase a woman's life length