1. One Sample T-tests
One sample t-tests are used in the following two situations
The size of a sample is less than 25
The population standard deviation is unknown
The formula for a one sample test uses the estimated population standard deviation to calculate the standard error
𝜎 𝑀 = 𝜎 𝑒𝑠𝑡 𝑛
𝑡= 𝑀−𝜇 𝜎 𝑀

2. Estimated Standard Error
The estimated standard error uses the estimated population standard deviation
This formula has a correction factor in the denominator of -1
𝜎 𝑒𝑠𝑡 = (𝑋−𝑀) 2 𝑛−1

3. Region of Rejection and Retention
Determining whether or not to reject the null depends on where the obtained t value falls within the t-distribution
A t score that is close to 0 will likely be in the region of retention
A t score that is far from 0 will likely be in the region of rejection

4. Directional Tests
One tailed tests place the entire region of rejection in a single tail
Two tailed tests divide the region of rejection into portions for each tail

5. t-Distributions
The shape of the t-distribution changes depending upon the size of your sample