The Human Resources (HR) group gives job applicants at a firm a personality test

Question

The Human Resources (HR) group gives job applicants at a firm a personality test to assess how well they will fit into the firm and get along with colleagues. Historically, test scores have been normally distributed with mean and standard deviation =30. The HR group wants to hire applicants whose true personality rating mu is greater than 178 points. (Test scores are an imperfect measure of true personality.) Use this information to answer parts a through c below.

(a) Before seeing test results, should the null hypothesis of the HR group assert that for an applicant is greater than 178 or less than 178? H0: __ 178

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(b) If the HR group chooses the null hypothesis found in part a, then for what test scores (approximately) will the HR group reject H0 if =5%?

If =5%, the HR group will reject H0 for test scores greater than _______. (Round to the nearest whole number as needed.)

(c) What is the chance for a Type II error using the procedure in part b if the true score of an applicant is196?

The chance for a Type II error using the procedure in part b if the true score of an applicant is196 is about ______. (Round to three decimal places as needed.)

Explanation / Answer

The null hypothesis is that the score > 178

Thus, we perform a one tailed test

Z-critical value for the one tailed test at 95% confidence = 1.64

The HR group will reject people whose score is below 178 - 1.64(30) = 128.8 i.e 129

Now, beta or the probability of the type two error = 1 - P ( Z > 129 - 196 / 30)

= 0.01276

Thus, there is only 1.276 % chance of type 2 error

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