When to Use This Version

We would use this version of hypothesis testing in any of the following situations:

• We know what the population standard deviation $\sigma$ is.
• We have an estimate of the population standard deviation from some other source that is considered reliable enough to assume that this is the true population standard deviation $\sigma$ .

Assumptions The following assumptions are made:

• 1) The sample is obtained using simple random sampling
• 2) At least one of the following statements is true:
  • The data are normally distributed
  • The sample size $n$ is $30$ or more (the central limit theorem applies)