The T-Distribution is a distribution we can use when performing inference tests (confidence intervals or hypothesis tests) on the mean. There are several assumptions that need to be met before we use the T-distribution, which are listed below: The population standard deviation, is unknown The data comes from a distribution that is approximately Normal (This is important if we have a smaller sample size) The data set contains no outliers (This is also important, as it may indicate the data is not Normal, and have a large impact on the estimate of standard deviation) The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom (df). When you use a t-distribution to estimate the population mean, the degrees of freedom are equal to n-1. So, the critical T values used will be dependent on the sample size, and account for the additional variability from using the sample standard deviation as opposed to the population standard deviation. When we run a hypothesis test, the over-arching process will remain the same regardless of distribution that we use. The steps to run a hypothesis test for the sample mean using the T-distribution are as follows: Step 1: Write out your hypotheses based on the words given in the problem Step 2: Determine your value of alpha Step 3: Compute your T statistic Step 4: Compare the T-statistic with the critical T-value, or compute the P-value Step 5: Make your conclusion