The GPA of a first semester freshmen at State University has an unknown mean of u and known standard deviation o = 0.65. We wish to create a confidence interval for u. We randomly select 12 first semester freshmen at State University and calculate their GPA. The sample mean was x = 2.82 and the sample standard deviation was s = 0.7755. a)What is the critical value for a 98% confidence interval for u? b) Create a 98% confidence interval for u c) How long is the 98% confidence interval for u? d) How many observations would we need to guarantee that the 98% confidence interval above has a length of 0.4 or less? e) Create a 98% prediction interval for / using this data. f) Assuming o is not known, create a 98.0% confidence interval for / using this data. g. What is the length of the confidence interval for part f