The Sudoku puzzle has recently become very popular all over the world. It is based on a 9 x 9 grid and the challenge is too ill in the grid so that every row, every column, and every 3 x 3 box contains the digits 1 through 9. A researcher is interested in estimating the average time taken by a college student to solve the puzzle. He takes a random sample of 8 college students and records their solving times as 14, 7, 17, 20, 18, 15, 19, 28 minutes.

a. Construct the 99% confidence interval for the average time taken by a college student to solve a Sudoku puzzle.

b. What assumption is necessary to make this inference?