1% significance level. 9 Suppose that a military dictator in an unnamed country holds a plebiscite (a yes/no vote of confidence) and claims that he was supported by 65% of the voters. A human rights group suspects foul play and hires you to test the validity of the dictator's claim. You have a budget that allows you to randomly di Wibom sample 200 voters from the country. no bn (i) Let X be the number of yes votes obtained from a random sample of 200 out of the entire voting population. What is the expected value of X if, in fact, 65% of all voters supported the dictator? (ii) What is the standard deviation of X, again assuming that the true fraction voting yes in the plebiscite is .65? (iii) Now, you collect your sample of 200, and you find that 115 people actually voted yes. Use the CLT to approximate the probability that you would find 115 or fewer yes votes from a random sample of 200 if, in fact, 65% of the entire population voted yes. (iv) How would you explain the relevance of the number in part (iii) to someone who does not have training in statistics? 14h 1994 major league baseball season, Tony Gwynn of the San Diego about whether against 11 Suppose that between their first and second years in college, 400 students are randomly selected and given a university grant to purchase a new computer. For student i, y; denotes the change in GPA from 1.27, is the first year to the second year. If the average change is y = .132 with standard deviation s = the average change in GPAs statistically greater than zero? 12 (Require variable on nonnegative integer values, 10.12. 1S