What is the condition for using a t-test or a z-test?

T-test is usually used when we have a sample size of less than 30 and z-test when we have a sample test greater than 30.

The decision to use a t-test or a z-test depends on certain conditions related to the data and the context of the analysis:

1. Sample Size: If the sample size is large (typically n > 30), it’s appropriate to use a z-test because the sampling distribution of the sample mean approaches a normal distribution due to the Central Limit Theorem. For smaller sample sizes (typically n < 30), a t-test is more appropriate because the t-distribution better approximates the sampling distribution of the sample mean.
2. Population Variance: If the population variance is known, a z-test can be used. However, if the population variance is unknown (which is often the case), a t-test is preferred.
3. Data Distribution: The t-test assumes that the data are normally distributed, but it is robust to moderate departures from normality, especially for large sample sizes. The z-test also assumes normality.
4. Type of Data: If you are comparing means from two independent groups, you would typically use a two-sample t-test (or z-test if the conditions are met). If you’re comparing the mean of a single group to a known value, a one-sample t-test (or z-test) is appropriate.

In summary, if the conditions for using a z-test are met (large sample size, known population variance, and normally distributed data), then you can use a z-test. Otherwise, a t-test is more appropriate. However, it’s essential to assess the specific characteristics of your data and the assumptions of each test before making a decision.