Mastering statistical techniques can help us to better understand the world around us, and learning to handle data correctly can prove useful in a variety of careers. T-Tests can help to determine whether or not the difference between an expected set of values and a given set of values is significant. While this procedure may look difficult at first, it can be simple to use with a little bit of practice. This process is vital to interpreting statistics and data, as it tells us whether or not the data is useful.

### Procedure

State the hypothesis. Determine whether the data warrants a one-tailed or two-tailed test. For one-tailed tests, the null hypothesis will be in the form of μ > x if you want to test for a sample mean that is too small, or μ < x if you want to test for a sample mean that is too large. The alternative hypothesis is in the form of μ = x. For two-tailed tests, the alternative hypothesis is still μ = x, but the null hypothesis changes to μ ≠ x.

Determine a significance level appropriate for your study. This will be the value you compare your final result to. Generally, significance values are at α = .05 or α = .01, depending on your preference and how accurate you want your results to be.

Calculate the sample data. Use the formula (x - μ)/SE, where the standard error (SE) is the standard deviation of the square root of the population (SE = s/√n). After determining the t-statistic, calculate degrees of freedom through the formula n-1. Enter the t-statistic, degrees of freedom, and significance level into the t-test function on a graphing calculator to determine the P-value. If you are working with a two-tailed T-Test, double the P-value.

Interpret the results. Compare the P-value to the α significance level stated earlier. If it is less than α, reject the null hypothesis. If the result is greater than α, fail to reject the null hypothesis. If you reject the null hypothesis, this implies that your alternative hypothesis is correct, and that the data is significant. If you fail to reject the null hypothesis, this implies that there is no significant difference between the sample data and the given data.

#### Tip

Always double check your calculations.

#### Warning

T-Test results are subjective to the significance level you choose to compare your results to. Although results are accurate most of the time, it is still possible to misinterpret the data.