St. Norbert's College in Green Bay, Wisconsin, and Wisconsin Public Radio conduct an annual poll of Wisconsinites about political opinions. The Fall 2011 survey asked a random sample of 402 adult Wisconsin residents whether they think things in the country are going in the right direction or in the wrong direction. 66% said that things were going in the wrong direction.
a) Calculate the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence.
b) Would the margin of error be larger or smaller for 95% confidence? Explain.