The data generated represents 100 students at the University of Utah who have their heights measured. Your friend bets you that the average height of the students is 67 inches. Assume that you and your friend suppose the true standard deviation, , is 3.5 inches. Write an appropriate set of null and alternative hypotheses about the true average height of the students. What is the appropriate statistical test to carry out? What do you need to assume to do this test? Complete the test at the 95% significance level and analyze your results.