![standard normal table t test standard normal table t test](https://cnx.org/resources/f96bb896da4d8fe64330685b719e39eb13f0a3c6/ttableimage.gif)
Consequently, a small sample size refers to a sample size that is less than thirty, that is, n ˂ 30, with n denoting the sample size. A large sample size, in this case, refers to a sample size that is greater than thirty, that is, n ˃ 30. On the other hand, the t-test is used in hypothesis testing when the sample size is small. Notably, the z-test is used in hypothesis testing when the sample size is large. While sample sizes differ from analysis to another, there is a suitable test of hypothesis for any sample size. Notably, the population standard deviation is estimated from dividing the sample population standard deviation by the square root of the sample size. However, with the t-score calculation dependent on the population variance, we can always estimate the population variance given the standard deviation or variance of the sample mean and sample size. While the population variance in the z-test is known, the population variance in the t-test is unknown. While using both the t-test and z-test in the testing of the hypothesis, the population variance plays a major role in obtaining both the t-score and z-score. On the other hand, the z-test is based on Normal distribution. Notably, the t-test is based on the Student t-distribution. However, the two tests use different distribution types. Type of Distributionīoth the t-test and z-test employ the use of distributions to compare values and reach conclusions in the testing of the hypothesis. The following are the key differences between the t-test and the z-test of the hypothesis. While the two statistical methods are commonly involved in the analysis of data, they largely differ from their application, formulae structure, and assumptions amongst other differences.
![standard normal table t test standard normal table t test](https://cdn.scribbr.com/wp-content/uploads/2020/11/standard-normal-distribution-of-sleep-duration.png)
Main Differences Between T-Test and Z-Test The z-test is a univariate test that is based on the standard normal distribution.
![standard normal table t test standard normal table t test](https://cdn.analyticsvidhya.com/wp-content/uploads/2019/05/t-table.png)
On the other hand, the z-test is the hypothesis test that ascertains if the averages of two sets of data differ from each other being given the variance or standard deviation. The standard deviation of the population is estimated by dividing the standard deviation of the sample by the square root of the population size. The t-test is based on Student t- statistic, having the mean being known and the variance of the population approximated from the sample. The t-test is a parameter applied to an identity to identify how the data averages differ from each other when the variance or standard deviation is not given. For large sample sizes and known standard deviation. For limited sample sizes, not exceeding thirty. Distribution of z is assumed to be normal, with a mean of zero and a variance of one. Sample values are accurately collected and recorded. All data points are assumed to be independent.
![standard normal table t test standard normal table t test](https://i.ytimg.com/vi/9KOJtiHAavE/maxresdefault.jpg)
Key Assumptions All data points are assumed, not dependent. Comparison Table Between T-Test and Z-Test Parameter of Comparison T-Test Z-Test Type of Distribution Student t-distribution Normal distribution Population Variance Suitable for unknown population variance. A T-test is best with the problems that have a limited sample size, whereas Z-test works best for the problems with large sample size.