This statistic is used to test hypotheses about an UNKNOWN population mean (μ), when the value of the population standard deviation (σ) is unknown. The formula for the t-statistic is similar to the formula for the z-statistic, except instead of using standard error (σ_{M}), the estimated standard error (s_{M}) is used.

t = (M-μ)/s_{M} = (M-μ/(√s²/n)

Two basic assumptions for a hypothesis test done using the t statistic:

1) The values in the sample must be independent observations meaning an occurrence of one value does not have an influence on the occurrence of the second value.

2) The population being sampled must be normal. NOTE: if the population distribution is suspected to be not normal than a larger sample size n is needed to determine the true nature of the distribution.

The t statistic does not require any prior knowledge about the population mean or variance. A t statistic, in this way, is much more equipped to handle hypothesis testing theoretical predictions.

ex. Using a rating scale to measure how people feel about controversial issues. Using a scale of 1-7, where 4 indicates a neutral position, the population mean, μ, will be equal to that value. The null hypothesis then would be that the average value of the population shows no preference for controversial issues by logic.

Steps for using a t statistic to solve a hypothesis test:

1) Establish H_{0}, H_{I}, and α.

2) Locate the critical region using the degrees of freedom (df) and the t-distribution table.

3) Calculate the test statistic by computing s², s_{M}, and the t statistic. They should be found in that order.

4) Now a decision can be made about the H_{0}.