A mathematics faculty member claims that the average score on statistics final exams at their college is greater than 80. To test this claim you randomly select 15 final exams from students at the college. The sample has a mean of 84.4 and a standard deviation of 7.6. The population is assumed to be normal. At = 0.05, do you have enough evidence to support the faculty member's claim? (15 points) a. State the hypotheses. b. Calculate the standardized test statistic. Show the calculation. c. Find the P-value. Round to 3 decimal places. d. Sketch the P-value for the hypothesis test. e. Make decision about the hypotheses and answer the research question in the