One Sample T-Test

One sample t test is to answer whether your group comes from a different population than the one specified.

The problem is that if you calculate a sample mean and it is different from the one hypothesized, there are two possible reasons for the difference:

         Your sample comes from a different population and the sample mean represents a different population mean. When this happens, you reject the Null Hypothesis.

         The group comes from the same population and the mean varies by chance. You just happened to pick up such a sample. When this happens, you did not reject the Null Hypothesis.

Using one sample t-test, comparing the sample mean to the population mean, to get an estimate of the probability that the sample mean is different by chance.


The variable should be normally distributed, which can be evaluated by looking at the distribution of the data (via histograms, box plot, or QQ plot) or by performing a normality test.


Below is the sample input window




Below is the sample output and explanation of the above model:


t test comparing sample mean to populational mean


One Sample t-test


(1) T test for BMI comparison to true mean: 22



data: BMI

t = -7.3697, df = 657, p-value = 5.158e-13

alternative hypothesis: true mean is not equal to 22


(2)    Observed mean and its 95% confidence interval


95 percent confidence interval:

21.18059 21.52537

sample estimates:

mean of x




Empower also output following box plot to show the means and distribution.