1. The problem asks: What is a z test and when do we use it? 2. A z test is a statistical test used to determine if there is a significant difference between sample and population means or between two sample means when the population variance is known. 3. The formula for the z test statistic is: $$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$ where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. 4. Important rules: - Use a z test when the population variance is known. - The sample size should be large (usually $n \geq 30$) or the population should be normally distributed. 5. We use the z test to check hypotheses about population means, such as testing if a sample mean differs significantly from a known population mean. 6. In summary, the z test helps us decide if observed data is consistent with a hypothesized population parameter when variance is known and sample size is sufficient.