Question

A personal specialist of a major corporation is recruiting a large number of employees for an overseas assignment. During the testing process, the management inquires the mean of the scores from the specialist and the reply was 90. When the management reviews 20 of the test results compiled,it finds that the mean score is 84, and the standard deviation of 67 compiled,it finds that the mean score is 84, and the standard deviation of this score is 11. If the management wants to test the specialist’s view at 1%significant level,what decision can be drawn?

Answer 1

The specialist's result says that the mean = 90. But the management wants to test it. That is check whether the true mean is same or different from 90. Since we do not know the population standard deviation, we will use the t-dist.

Test

Test Statistic:

Null mean = 90

Note: there are two values for SD given 67 and 11. The test results will be given for both.

SD = 67	SD = 11
Test Stat = -0.40	Test Stat=-2.439

Level of significance = 0.01

Critical value at 0.01 using t-dist tables with df = 19 and p = 0.005

Critical value = 2.861

SD = 67	SD = 11
|Test Stat| < Critical value	|Test Stat| < critical value

At both values we reach at the same conclusion.

We do not reject the null hypothesis at 1% level and conclude that the true mean is significantly 90.