The authors of the paper "Movie Character Smoking and Adolescent Smoking: Who Matters More, Good Guys or Bad Guys?" (Pediatrics [2009]: 135-141) classified characters who were depicted smoking in movies released between 2000 and 2005. The smoking characters were classified according to sex and whether the character type was positive or negative. It turned out that out of the 110 male characters, 78 were negative, while out of the 111 females, 68 were negative. Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. (a) Is it true that male movie characters who smoke tend to be negatively portrayed more frequently than their female counterparts? (b) Interpret in the context of the study the p-value you computed in part (a). (c) Based on your answer to the hypothesis test in part (a), explain in the context of the study what type(s) of error(s)(Type I, Type II, or both) you could have made. Justify your answer. (d) Construct a 70% confidence interval for the difference in the true proportion of movie characters who smoke who are negative characters between the two groups. (e) Interpret in the context of the study the confidence interval you constructed in part (d).