# T Test on a column of Data

The MINITAB TTEST command is used to determine if the true mean of a column is different from a hypothesized mean. In the case of our column which contains the improvement from TEST 1 to TEST 4, we might wish to know if there actually has been an improvement from one test to the other. To test this, we could test whether the improvement column is different from zero. It is possible that scores actually went down from TEST 1 to TEST 4. A two-sided T-TEST would use the null hypothesis that the improvement is different from zero, negative or positive. A one-sided test would test that the improvement is different from zero, and furthermore is positive or negative depending upon the hypothesis.

The syntax of the T Test in MINITAB is the following.

`TTEST hypothesized-mean column`

A T Test on the improvement column, column 6, would be the following.

MTB> TTEST 0 C6

TEST OF MU = 0.00 VS MU N.E. 0.00

N MEAN STDEV SE MEAN T P VALUE

IMPROV 20 2.90 14.56 3.26 0.89 0.38

We see that our improvement variable was computed using 20 cases. The mean is 2.90, the standard deviation is 14.56. The standard error of the mean, which is used in computing the T statistic, is 3.26. The calculated T value is .89. The P value determines the significance of the calculated T without having to refer to tables. We would reject the null hypothesis that the true mean of the improvement variable is zero in favor of the alternative hypothesis that the true mean is different from zero when the P value is less than .05, for 5% alpha level (or 95% confidence level). Since the P value is .38, we would not reject the null hypothesis and cannot conclude that test scores changed from the first test to the fourth test. This is consistent with our confidence interval results.