To determine the efficiency of a batch of production of electric motors, 10 motors are tested. The average efficiency of the sample is calculated to be 91.0%, and the standard deviation of the sample is 0.8 percentage point.
(a) Determine a 95% confidence interval for the mean efficiency of the given batch of motors.
(b) If we want to cut the confidence interval to one-third, how many more motors should be tested?