Question

An industrial and organizational psychologist hypothesizes that applied mathematicians, such as actuaries, are less extroverted than the general population. To test his hypothesis, he recruits applied mathematicians into a study (assume it is a simple random sample) and obtains 21 completed questionnaires measuring the Big Five dimensions of personality (neuroticism, extroversion, openness to experience, agreeableness, and conscientiousness).

Personality dimensions measured by the instrument are normally distributed in the general population, and are reported as ?t‑scores, with a mean of 50 and a standard deviation of 10. He posits null and alternative hypotheses for the average extroversion score of all mathematicians, ?μ.

?0:?=50,H1:μ<50

What is the maximum mean extroversion score in his sample that would be required to reject his null hypothesis at a significance level of 0.05? Give your answer precise to two decimal places.

?⎯⎯⎯=

Answer 1

solution: © from the given data Hoi 4:50 HiM 2.50 n =21 1 S-10 dla = n-1 = 21-1 df = 20 0.05 + (/idf) 2 poos/ ,20) -1.725 NOW) a ta < -1.725 a so = -1.725 10/zi W-50 = -3.76426 2 46.2374 a 2146.24