T Distribution in Hypothesis Testing
As an analyst in the industry, when you would use hypothesis testing, the standard deviation of the population would be unknown most of the times. So how would you proceed in such a scenario? Let us find out.
A t-distribution is also referred to as Student’s T distribution. A t-distribution is similar to the normal distribution in many cases; for example, it is symmetrical about its central tendency. However, it is shorter than the normal distribution and has a flatter tail, which would eventually mean that it has a larger standard deviation.
At a sample size beyond 30, the t-distribution becomes approximately equal to the normal distribution.
The most important use of the t-distribution is that you can approximate the value of the standard deviation of the population (σ) from the sample standard deviation (s). However, as the sample size increases more than 30, the t-value tends to be equal to the z-value. Thus, if you want to summarise the decision-making in a flowchart, this is what you would get.
Let’s look at how the method of making a decision changes if you are using the sample’s standard deviation instead of the population’s. If you recall the critical value method, the first step is as follows:
Calculate the value of Zc from the given value of α (significance level). Take it as 5% if not specified in the problem.
So, to find Zc, you would use the t-table instead of the z-table. The t-table contains values of Zc for a given degree of freedom and value of α (significance level). Zc, in this case, can also be called as t-statistic (critical).
In the second question, you used the t-table to find the value of Zc for sample size = 32 and a significance level of 5%. If you use the z-table for the same, you would get the same value of Zc, since, for sample size ≥ 30, the t-distribution is the same as the z-distribution.
Practically you would not need to refer to the z-table or t-table when doing hypothesis testing in the industry. Going forward when you need to do hypothesis testing in demonstrations of Excel or R, you would use the term t-test since that is mostly performed in the industry. All calculations and results of a t-test are same as the z-test whenever the sample size ≥ 30.