When to Use This Version

We would use this version to test a claim made about the proportion of individuals that have a certain characteristic in a population.

This is actually a special case of "known $\sigma$ " because when the assumptions regarding sample size are met,
we can calculate the population standard deviation from the population proportion:

Under the sample size assumptions, if the true population proportion is $p_0$ , then the population standard deviation is

$$\sqrt{p_0\cdot(1-p_0)}$$

Assumptions The following assumptions are made:

1) The sample is obtained using simple random sampling

2) $n\cdot p_0\cdot(1-p_0)\geq10$ , where $p_0$ is the population proportion when the null hypothesis is true.
Cell $B11$ will contain the word "Valid" when this assumption is met.

3) The sample represents at most $5\%$ of the total population $(n\leq0.05N)$ .