a Type II error.
Rolls of material, manufactured by a machine, contain defects at a mean rate of 6 per roll.
The machine is modified. A single roll is selected at random and a test is carried out to see whether or not the mean number of defects per roll has decreased. The significance level is chosen to be as close as possible to \(5 \%\).
(b) Calculate the probability of a Type I error for this test.
(c) Given that the true mean number of defects per roll of material made by the machine is now 4, calculate the probability of a Type II error.