Question

A group of researchers are interested in the effects of a special training session on student performance on a standardized test.  Under normal circumstances the mean score on the test is 100 with a standard deviatin of 15.  The students who receive the special training score as follows:

90 110 120 95 105 140 70 125 110 105 123 111 122 98 100

In a spread sheet, like microsoft excel

Answer 1

For the given values, we first compute the sample mean here as:

As we are testing here whether the mean score has increased on the test from 100, therefore the test statistic here is computed as:

As we want to check here whether the mean has increased, therefore this is a one tailed test for which the p-value is obtained from the standard normal tables as:
p = P(Z > 2.13) = 0.0164

As the p-value here is 0.0164 < 0.05 which is the general level of significance to do these tests, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that there is a positive effect of special training session on the student performance here.