Question 2

The executive director of a company is recruiting graduate trainees from two universities. The performance index follows normal distribution. The variance of performance index of trainees from University I is 12 and variance for University II is 7. The manager feels that the mean performance index of trainees from University I is less than that of trainees from University II. In order to test hypothesis, he has selected a sample of 60 trainees from University I and their mean performance index is found to be 10. On the other hand, he has selected a sample of 69 trainees from University II, and their mean performance index is found to be 8.5. Test manger's intuition at 5% significance level.