# 8.2.3 - Hypothesis Testing

In this section we will be comparing one sample mean to one known or hypothesized population value. In Lesson 5 you learned how to conduct randomization tests. Here, you will learn how to conduct a one sample mean $$t$$ test and a one sample mean $$z$$ test. The $$t$$ distribution is used to estimate the sampling distribution when the sample size is large (at least 30) or when the population is known to be normally distributed (but $$\sigma$$ is unknown). The $$z$$ distribution is used on rare occasions when the population is normal and the population standard deviation is known. Note that for this course the one sample mean $$z$$ test is optional; it used only in specific cases where the population is known to be normally distributed and when the population standard deviation ($$\sigma$$) is known. The most commonly used one sample mean test is the "one sample mean $$t$$ test" which is also known as a "single sample mean $$t$$ test."