The midterm exam scores of 100 randomly selected FCBE MIS students studying the course MIS 7700 from the population are normally distributed with a mean of 46 out of 50. It is known that mean score for all the MIS 7700 FCBE MIS students is 45 on an average with a standard deviation of 5. You want to test the statement: "The sample is performing significantly different than the average score of MIS 7700 FCBE MIS student." (a) Do you use a one-tailed or a two-tailed test? Why? (0.5 Points) (b) What are your null and alternate hypotheses? In plain English, explain what are your type I and type II errors in this case? (1 Point) (c) Would you reject your null hypothesis at the 5% level? How about the 10%, 2% and 1% levels? (2 points) (d) In the example above, suppose the margin of error (how many percentage points your sample differs from the population) is 1 and investigator plans to use the 95% confidence interval. Determine the minimum sample size required in this case. (1.5 points) Hint: Refer to how confidence interval is calculated and how sample size determines the confidence interval