Question

1.
a) For a test at a fixed significance level, and with given null and alternative hypotheses, what will happen to the power as the sample size increases?
b) For a test of a given null hypothesis against a given alternative hypothesis, and with a given sample size, describe what would happen to the power of the test if the significance level was changed from 5% to 1%.
c) A test of a given null hypothesis against a given alternative hypothesis, with a sample of size n and significance level of , has power of 80%. What change could I make to the test to increase my chance of rejecting a false null hypothesis?
d) How can we attain a test which has a very low probability of Type I error and also a very low probability of Type II error?

Answer 1

(a) Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false. Thus, it increases the power of the test.

(b) The power of the test would increase if the significance level was changed from 5% to 1%.

(c) Increase the sample size

(d) This is not possible because when the Type I error increases, the Type II error decreases and vice versa.