# 8.1.2 - Hypothesis Testing

A hypothesis test for a proportion is used when you are comparing one group to a known or hypothesized population proportion value. In other words, you have one sample with one categorical variable. The hypothesized value of the population proportion is symbolized by $$p_0$$ because this is the value in the null hypothesis ($$H_0$$).

If $$np_0 \ge 10$$ and $$n(1-p_0) \ge 10$$ then the distribution of sample proportions is approximately normal and can be estimated using the normal distribution. That sampling distribution will have a mean of $$p_0$$ and a standard deviation (i.e., standard error) of $$\sqrt{\frac{p_0 (1-p_0)}{n}}$$

Recall that the standard normal distribution is also known as the z distribution. Thus, this is known as a "single sample proportion z test" or "one sample proportion z test."

If $$np_0 < 10$$ or $$n(1-p_0) < 10$$ then the distribution of sample proportions follows a binomial distribution. We will not be conducting this test by hand in this course, however you will learn how this can be conducted using Minitab Express using the exact method.