Referring to Example 13, conduct a test to show that the mean change \(\mu_{D}\) is different from 0 . Take \(\alpha=0.05\).

Data From Example 13

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EXAMPLE 13 The chi square test of independence To determine whether there really is a relationship between an employee's perfor- mance in the company's training program and his or her ultimate success in the job, the company takes a sample of 400 cases from its very extensive files and obtains the results shown in the following table: Performance in training program Below average Average Above average Total Poor 23 60 29 112 Success in job (employer's rating) Average 28 79 60 167 Very good 9 49 63 121 Total 60 188 152 400 Use the 0.01 level of significance to test the null hypothesis that performance in the training program and success in the job are independent.