How to perform a Z-test?

To perform a Z-test, first state the null and alternative hypotheses and determine the significance level.

A Z-test is a statistical test used to determine whether the mean of a sample is significantly different from a known population mean. It is used when the sample size is large (n > 30) and the population standard deviation is known. The first step in performing a Z-test is to state the null and alternative hypotheses. The null hypothesis (H0) is that there is no significant difference between the sample mean and the population mean, while the alternative hypothesis (Ha) is that there is a significant difference.

Next, determine the significance level (α), which is the probability of rejecting the null hypothesis when it is actually true. The most common significance level is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.

To calculate the Z-score, use the formula:

Z = (x̄ - μ) / (σ / √n)

where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. The Z-score represents the number of standard deviations that the sample mean is from the population mean.

Finally, compare the calculated Z-score to the critical value from the Z-table at the chosen significance level. If the calculated Z-score is greater than the critical value, reject the null hypothesis and conclude that there is a significant difference between the sample mean and the population mean. If the calculated Z-score is less than the critical value, fail to reject the null hypothesis and conclude that there is no significant difference.