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 – 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.

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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.

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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.