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Please write a Paragraph answering to this discussion below with your opinion. Please include citations and references in alphabetical order in case of another source.

To know when to use a t-test vs. a z-test, first we need to define each of them. “A t-test is used to examine how the means taken from two independent samples differ…Z-test refers to a univariate statistical analysis used to test the hypothesis that proportions from two independent samples differ greatly.” (Surbhi, 2018)

Essentially there are similarities in the information found in the two tests, the choice of which to use is based on the following parameters.

1. The number of items: If it is large (over 30) it is better to use a z-test, if it is small (under 30) it is better to use a t-test.

2. If the variance or standard deviation is known, use a z-test, and if it is unknown, use a t-test.

“The difference between t-test and z-test can be drawn clearly on the following grounds:

1. The t-test can be understood as a statistical test which is used to compare and analyze whether the means of the two population is different from one another or not when the standard deviation is not known. As against, Z-test is a parametric test, which is applied when the standard deviation is known, to determine, if the means of the two datasets differ from each other.
2. The t-test is based on Student’s t-distribution. On the contrary, z-test relies on the assumption that the distribution of sample means is normal. Both student’s t-distribution and normal distribution appear alike, as both are symmetrical and bell-shaped. However, they differ in the sense that in a t-distribution, there is less space in the center and more in the tails.
3. One of the important conditions for adopting t-test is that population variance is unknown. Conversely, population variance should be known or assumed to be known in case of a z-test.
4. Z-test is used to when the sample size is large, i.e. n > 30, and t-test is appropriate when the size of the sample is small, in the sense that n < 30.” (Surbhi, S, 2018)

Both the t-test and the z-test will give similar information. The amount of data and the distribution are the keys to determining which way the information is calculated.

References:

Surbhi, S. “Difference Between t-Test and z-Test (with Comparison Chart).” Key Differences , 20 Mar. 2018, keydifferences.com/difference-between-t-test-and-z-test.html.