Z-Test

A z-test is a method of hypothesis testing in which the test statistic is compared with the standard normal distribution. For a mean, the statistic is $z = (\bar{x} - \mu_0) / (\sigma / \sqrt{n})$, where $\bar{x}$ is the sample mean, $\mu_0$ the value stated in the null hypothesis, $\sigma$ the standard deviation and $n$ the sample size. The test is appropriate when the population standard deviation is known or the sample is large enough for the central limit theorem to apply. For small samples with an estimated standard deviation, a test based on Student's t-distribution is used instead.

Suppose 400 daily returns of a strategy have a mean of 0.08 percent and a standard deviation of 1.2 percent. The standard error is $1.2 / \sqrt{400} = 0.06$, so $z = 0.08 / 0.06 = 1.33$. This is below the two-sided 5 percent critical value of 1.96, so a true mean of zero cannot be ruled out.