Question

According to a​ report, the standard deviation of monthly cell phone bills was ​$49.51 three years ago. A researcher suspects that the standard deviation of monthly cell phone bills is less today. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error.

Answer 1

a) As we are testing here whether the standard deviation less than 49.51, therefore the null and the alternative hypothesis here are given as:

These are the required set of hypothesis here.

b) Type I error is the rejection of a true null hypothesis. Therefore here type I error would occur, if we conclude that the standard deviation is less today even though it it not.

c) Type II error is the non rejection of a false null hypothesis. Therefore here type II error would occur, if we conclude that there is no reduction in standard deviation today even though it has decreased.