Even in states where support for the death penalty has historically been strong, political leaders have begun to consider eliminating the death penalty. For example, in October of this year, the Oklahoma House Judiciary Criminal Committee met to discuss the possibility of recommending a moratorium on executions. Those concerns about the death penalty extend to the populace as a whole. Evidence on the views of Americans on the death penalty is provided by the results of a poll of $1009$ adults conducted from October $2$nd $-23$rd by the Gallup Organization. In that poll those surveyed were asked "Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today." Of the $1009$ adults surveyed, $474$ indicated that they believe the death penalty is applied fairly in the U$.$S$.$a$)$ Estimate p$,$ the proportion of adults in the population who believe the death penalty is applied fairly in the U$.$S$.$ Give the bias and the mean squared error of your estimator.b$)$ Give a $97$ percent confidence interval for p$.$c$)$ Test the hypothesis corresponding to the perception of some politicians that less than a majority of adults in the population feel the death penalty is applied fairly in the U$.$S$.$ Use a $4\%$ level of significance $(=0\mathrm{.}04).$