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

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

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

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

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