Posted: April 5th, 2017

A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. For each significance level, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student’s t-test which has separate critical values for each sample size. Therefore, many statistical tests can be conveniently performed as approximate Z-tests if the sample size is large or the population variance known. If the population variance is unknown (and therefore has to be estimated from the sample itself) and the sample size is not large (n < 30), the Student’s t-test may be more appropriate.

Nuisance parameters should be known, or estimated with high accuracy. Z-tests focus on a single parameter, and treat all other unknown parameters as being fixed at their true values. The test statistic should follow a normal distribution Z-test and T-test are statistical tests used to determine whether two population means are different. Z- test is applied when the variances are known and the sample size is large (n 30), the standard deviation is unknown while z-tests assume that it is known. Z-test has a single critical value which makes it more convenient than the t-test which has separate critical values for each sample size.

1. Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T-distribution.

2. A T-test is appropriate when you are handling small samples (n < 30) while a Z-test is appropriate when you are handling moderate to large samples (n > 30).

3. T-test is more adaptable than Z-test since Z-test will often require certain conditions to be reliable. Also, T-test has many methods that will suit any need.

4. T-tests are more commonly used than Z-tests.

5. Z-tests are preferred than T-tests when standard deviations are known.

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