The Committee of $200,$ a professional organization of preeminent women entrepreneurs and

corporate leaders, reported the following: $60\%$ of women MBA students say, $$Businesses pay

their executives too much money$$ and $50\%$ of the men MBA students agreed. Does there appear

to be a difference in the proportion of women and men who say, $$Executives are paid too

much$?$ Explain the meaning of your answer. Your answers should show assumptions,

hypotheses, and conclusions.

a$)$ If the preceding percentages resulted from two samples of size $20$ each, is the difference

statistically significant at a $0\mathrm{.}05$ level of significance? Justify your answer.

b$)$ If the preceding percentages resulted from two samples of size $500$ each, is the difference

statistically significant at a $0\mathrm{.}05$ level of significance? Justify your answer.