3. State University requires an admission test of all its students. A simple random sample of 256 students from the University was selected to estimate the average test score of all University students. The average (mean) for the sample was found to be x =23.4 with a sample standard deviation of s =3.65. (16 pts) (a) Construct a 95% confidence interval for the average (mean) test score of all University students. (Be specific about which formula you would use) (b) Interpret this confidence interval in simple language. (c) Which of the following would result in a wider confidence interval for the average (mean) test score of all University students? (select all that apply) i) Maintain the confidence level at 95%, but increase the sample size. ii) Maintain the confidence level at 95%, but decrease the sample size. iii) Keep the sample size at 256, but increase the confidence level to 99%. iv) Keep the sample size at 256, but decrease the confidence level to 90%