A college admissions officer takes a simple random sample of 100 entering freshman and computes their mean mathematics SAT score to be 458. Assume the population standard deviation is 116. Use this information to answer questions 1 1-18. 1 1) Construct a 95% confidence interval for the population mean mathematics SAT score for the entering freshman class. 12) Interpret the 95% confidence interval created in question 1 1. 13) Construct a 99% confidence interval for the population mean mathematics SAT score for the entering freshman class. 14) Compare the 95% confidence interval (question 1 1) to the 99% confidence interval (question 13). Explain the difference between the two intervals. 15) Suppose that instead of taking a sample of size 100 a sample of size 200 was selected. Compute a 95% confidence interval with this larger sample size. 16) Compare the 95% confidence interval for a sample of 100 (question 1 1) to the interval created with a sample of 200 (question 15). Explain the difference between the two intervals. 17) Suppose that instead of a population standard deviation of 1 16 it was 85. Compute a 95% confidence interval with the smaller population standard deviation. 18) Compare the 95% confidence interval for a population standard deviation of 116 (question 1 1) to the interval created with a population standard deviation of 85 (question 17). Explain the difference between the two intervals