A statistics professor gives a quiz to 16 students and calculates a mean (x-bar) of 21 with an unbiased estimate of the standard deviation (s-carat) of 8.5. The professor already knew that his students were smarter than average, so he made an a priori prediction that they would score higher than the known mean () of 18. Assume that the data is interval/ratio and normally distributed and set at .05. SHOW ALL WORKING a. State the null hypothesis: b. State the alternative hypothesis: c. What is the appropriate statistical test? d. What is the significance level? e. What is the appropriate sampling distribution? f. What is the critical rejection region for the null hypothesis? g. Calculate the statistic and draw your conclusions