Explain what is meant by
(a) a Type I error,
(b) a Type II error.
Roger thinks that a box contains 6 screws and 94 nails. Felix thinks that the box contains 30 screws and 70 nails. In order to test these assumptions they decide to take 5 items at random from the box and inspect them, replacing each item after it has been inspected, and accept Roger's hypothesis (the null hypothesis) if all 5 items are nails.
(a) Calculate the probability of a Type I error.
(b) If Felix's hypothesis (the alternative hypothesis) is true, calculate the probability of a Type II error.