Question: A process producing bricks is known to give an output whose weights are normally dis­tributed with standard deviation 0.12 pounds. A random sample of sixteen bricks from to­day's output had mean weight 4.07 pounds.

(a) Find a 99% confidence interval for the mean weight of all bricks produced this day.

(b) Without doing the calculations, state whether a 95% confidence interval for the pop­ulation mean would be wider than, narrower than, or the same width as that found in (a).

(c) It is decided that tomorrow a sample of twenty bricks will be taken. Without doing the calculations, state whether a correctly calculated 99% confidence interval for the mean weight of tomorrow’s output would be wider than, narrower than, or the same width as that found in (a).

(d) In fact, the population standard deviation for today's output is 0.15 pound. Without do­ing the calculations, state whether a correctly calculated 99% confidence interval for the mean weight of today's output would be wider than, narrower than, or the same width as that found in (a).