An algebra i test contains 30 questions. some of the questions are worth 4 points each, and some are worth 2 points each. the total test is worth 100 points. let f represent the number of questions worth 4 points and t, the number of questions worth 2 points.

Arandom sample of 15 observations is used to estimate the population mean. the sample mean and the standard deviation are calculated as 172 and 63, respectively. assume that the population is normally distributed. a. with 99 confidence, what is the margin of error for the estimation of the population mean? b. construct the 99% confidence interval for the population mean. c. construct the 95% confidence interval for the population mean. d. construct the 83% confidence interval for the population mean. hint: you need to use excel function =t.inv.2t to find the value of t for the interval calculation.