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 = 25. The HR group wants to hire applicants whose true personality rating mean is greater than 200 points. (Test scores are an imperfect measure of true personality.)

(a) Before seeing test results, should the HR group assert as the null hypothesis that mean for an applicant is greater than 200 or less than 200?

(b) If the HR group chooses Ho: mean is less than or equal to 200, then for what test scores (approximately) will the HR group reject Ho if ∝= 2.5%

(c) What is the chance of a Type II error using the procedure in part (b) if the true score of an applicant is 225?