# Null Hypothesis and Type II Errors

Question

One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, mu, among the general population on this subsection. The website reports that mu is 142, but you believe that mu differs from 142. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 149 and that the standard deviation of their scores is 28.

Based on this information, answer the questions below.

Problem:

H0: mu = (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (142, 149, 128)

H1: mu = (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (142, 149, 128)

A Type II error is (rejecting, failing to reject) the hypothesis that mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (142, 149, 128) when, in fact, mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (142, 149, 128).

Suppose that you decide to reject the null hypothesis. What sort of error might you be making? (Type I, Type II)

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#### Solution Preview

H0: mu = 142

H1: mu not equal to 142

A Type II error is failing to reject ...

#### Solution Summary

The solution calculates the null hypothesis and type II errors for a personality test.