What conditions must be met for conducting a two-sample t test for the means?

Hint: Here, first we will understand the use of two – sample t test. Now, we will see the five different conditions that must be fulfilled for conducting a valid two – sample t test. Conditions related to distribution, information about the variances of the two samples etc. will be considered.

Complete step by step solution:
Here we have been asked to write the conditions that must be met for conducting a two – sample t test. First let us know about the two – sample t tests.
Now, in statistical mathematics the two – sample t test is also known as the independent samples t test. It is a method to test whether the unknown population means of two groups are equal or not. For a two – sample t test there must be two variables, the first one defines the two groups and the second one is the measurement of the interest. There are five conditions that must be fulfilled to conduct a valid two – sample t test.
(1) Data values must be independent, that means measurements for one observation must not affect the measurements of any other observation.
(2) Data in each group must be obtained by a random sample from the population.
(3) Data in each group must be normally distributed.
(4) Data values must be continuous.
(5) The variances for the two independent groups must be equal.
Hence, the above conditions are required.

Note: Note that there are certain types of t – test like: - one sample t – test, independent t – test, dependent t – test used for different purposes. Other than these tests there are many other tests also. In case if the variances for the two groups are not equal then also you can use the two – sample t test. In such cases we use a different estimation of the standard deviation.