When to Use This Version

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

• We have a sample of size $n_1$ taken from a population $1$ .
• We know the standard deviation of population $1$ is $\sigma_1$ .
• We have a sample of size $n_2$ taken from a population $2$ .
• We know the standard deviation of population $2$ is $\sigma_2$ .

Assumptions The following assumptions are made:

1) Both samples are obtained using simple random sampling

2) At least one of the following statements is true:

• The data are normally distributed
• The sample sizes $n_1$ and $n_2$ are both $30$ or more (the central limit theorem applies)