Note: For all hypothesis testing problems, please make sure that you write the hypotheses, test statistic, p-value, and conclusions in terms of the problem. 1. We are interested in estimating the proportion of students at a local university who smoke. Out of a random sample of 200 students from this university, 41 students smoke. (10 points total) (1) Calculate a 95% confidence interval for the proportion of students at this university who smoke and interpret this interval in context. N=200 p-hat= 41/200 =0.205 95% Conf. Interval= 0.205+10.205*0.795/200 x 1.96= {0.1490, 0.2609} (2) If we wanted the margin of error to be no larger than 2% at a 95% confidence level for the proportion of students who smoke, how big of a sample would we need? Margin of Error= 0.02 N=1565 I