Founded in 1890, the Literary Digest was a popular magazine in the early 1900s. The magazine correctly predicted the outcomes of the 1916, 1920, 1924, 1928, and 1932 presidential elections by conducting polls. With the Great Depression in full swing, the magazine ventured forth in 1936 to predict another presidential election outcome. Questionnaires were mailed out to more than 10 million adult Americans whose names and addresses they obtained from telephone books and vehicle registration lists. They received more than 2.4 million responses, with 57% of the responses indicating an intention to vote for Republican challenger Alf Landon over the Democratic incumbent Franklin Roosevelt. Theory based applet: http://www.isi-stats.com/isi2nd/ISIapplets2021.html a. Use the Theory-Based Inference applet to produce a 99.9% confidence interval for the proportion of all adult Americans who intended to vote for Alf Landon in 1936. Also interpret this interval. Option A: (0.5689,0.5711) Option B: (0.5789, 0.5811) b. Why is your interval from part (a) so narrow, even with an extremely large confidence level of 99.9%? Option A: because the sample size is to large, the confidence interval is very narrow Option B: any 99% confidence interval will be narrow Option C: the confidence interval is narrow by coincidence only Option D: because of the number of people who did not respond to the survey the confidence interval is low c. Alf Landon actually received 36.5% of the votes cast in the election. Does your 99.9% confidence interval include 0.365? Does it come close? Option A: yes, no Option B: no, no Option C: no, yes Option D: yes, yes