Nuclear power has always been a big topic of controversy. With the aftermath of the nuclear disaster at the Fukushima nuclear power plant in Japan, a poll was conducted here in the USA to determine the public's feelings on nuclear power. Let 1 p be the proportion of urban residents who support the construction of a nuclear power plant and let 2 p be the proportion of suburban residents who support the construction. In a random sample of 100 urban residents; 61 support the construction. In a similar survey of 120 suburban residents; 65 support the construction. a. At = 1%, perform a hypothesis test to test the claim that there is not a significant difference in the two population proportions. b. i. Find a 99% CI for the difference in the true proportion of urban residents and the true proportion of suburban ones who support nuclear power. ii. Does this confidence interval back up your response for the hypothesis test? Why