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 m and standard deviation σ = 25. The HR group wants to hire applicants whose true personality rating m 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 m for an applicant is greater than 200 or less than 200?
(b) If the HR group chooses H0: μ ≤ 200, then for what test scores (approximately) will the HR group reject H0 if α = 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?