Kamarie DeVoogd and Elliot Wood

A one-sample t-test for the mean is a type of hypothesis test that is used with quantitative variables to determine whether a sample comes from a population with a specified mean.  Sometimes the population mean is not known, so it will instead be a hypothesized mean.  It compares the difference between the observed statistic and a hypothesized value to the standard error of the observed statistic.  This can be expressed with the equation:  

The assumptions and conditions for the one-sample t-test for the mean are the same as for the on-sample t-interval.  If the conditions are met, we can proceed with the test.  

The t-value can be interpreted the same as a p-value.  If t< 0.05, we reject the null hypothesis, and accept the alternate hypothesis.  Therefore, if t > 0.05, we fail to reject the null hypothesis, and reject the alternate hypothesis because we have insufficient evidence to suggest otherwise.   

Generating a one-sample t-test for the mean in SPSS

• Go to the "Analyze" menu, hover over "Compare Means" to see a drop down menu, and select "One-Sample T Test".
• Drag the quantitative variable that you are testing to the "Test Variable(s)" box.
• Change the "Test Value" to the hypothesized value for your data, because this is the value that is being testing.
• Do not change any other options.
• Click "OK".
• The "One-Sample Statistics" chart and "One-Sample Test" chart will appear in the output window.
• In the "One-Sample Test" chart we can see our t value.  For the above example, t = 1.554. 

The following video illustrates these steps:

2014-11-19_2203