5.1 Answer true or false, with reasons if necessary.

(a) There is no way of reducing the probability of a Type I error without simultaneously increasing the probability of a Type II error.

(b) The probability of a Type I error is associated with an area under the distribution of X assuming the null hypothesis to be true.

(c) It is always desirable to minimise the probability of a Type I error.

(d) A larger sample, ceteris paribus, will increase the power of a test.

(e) The significance level is the probability of a Type II error.

(f) The confidence level is the probability of a Type II error.