Question 1) A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score above 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor have 90% confidence that the mean score for the class on the test would be above 70? Use an appropriate hypothesis test to determine if you are convinced that the professor would reach her goal? If you use a t-test, use df = 3. a) Identify relevant information Identify the appropriate numerical summary (center and spread) of the given data. State and check the assumptions required for the use of a hypothesis test. b) Express information in mathematical form State your H, and Ha H: H.: c) Develop a viable plan/Choose a mathematical model What statistical test do you plan on using? Why did you choose that statistical test? Please be specific and state your reason for choosing your statistical test. d) Execute a solution plan Perform the hypothesis test and show all work. (Don't forget the sketch) e) Draw a well-supported conclusion State your conclusion in the context of the problem.