One sample proportion tests and confidence intervals are covered in Section 6.1 of the Lock5 textbook.
In the last lesson you were introduced to the general concept of the Central Limit Theorem. The Central Limit Theorem states that if the sample size is sufficiently large then the sampling distribution will be approximately normally distributed for many frequently tested statistics, such as those that we have been working with in this course. When discussion proportions, we sometimes refer to this as the Rule of Sample Proportions. According to the Rule of Sample Proportions, if \(np\geq 10\) and \(n(1-p) \geq 10\) then the sampling distributing will be approximately normal. When constructing a confidence interval \(p\) is not known but may be approximated using \(\widehat p\). When conducting a hypothesis test, we check this assumption using the hypothesized proportion (i.e., the proportion in the null hypothesis).
If assumptions are met, the sampling distribution will have a standard error equal to \(\sqrt{\frac{p(1-p)}{n}}\).
This method of constructing a sampling distribution is known as the normal approximation method.
If the assumptions for the normal approximation method are not met (i.e., if \(np\) or \(n(1-p)\) is not at least 10), then the sampling distribution may be approximated using a binomial distribution. This is known as the exact method. This course does not cover the exact method in detail, but you will see how these tests may be performed using Minitab.