a. Construct and interpret a 99% confidence interval for the proportion of Americans who feel the country is headed in the right direction. (4 points) n15,n(1^)15 2500(,29)=725.2500(1.29)=1775 b. If the sample above was reduced from 2500 to 250 and everything else was the same above, the confidence interval would be (circle one) ( 1 point) a. Same Width b. Smaller Width c. Larger Width 2. Medical researchers measured the body temperatures of a randomly selected group of 125 adults and found a mean of 98.285 degrees with a standard deviation of 0.6824 degrees. a. Construct and interpret a 90% confidence interval for these data. (4 points) b. If we switched to a 99% confidence interval and everything else was the same as above, how would the width of the interval compare to part a. a. 99% confidence interval would be wider than the 90% confidence interval b. 90% confidence interval would be wider than the 95% confidence interval c. The intervals would have the same width. I am a lover of Men's basketball and I have watched every game this year with my cat, Bart. I think that Bart can now predict the winner of the games better than me (picks based first team He paws at on a piece of paper). I really want to see if Bart can pick the correct winner better than just guessing. Hence, I want to test if Bart is able to pick the winner more than 50% of the time at a 0.05 level of significance. Bart picked the winner correctly 40 of 68 games in the NCAA tournament last year. a. Write out the Null and Alternative Hypotheses (1 point) b. Calculate the Test Statistic. ( 2 points) c. What is the p-value? ( 1 point) d. What is your conclusion? ( 1 point)