Question

Why do you need to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means?

Short answer

It is important to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means because ${\mu }_1-{\mu }_2$ allows researchers to assess if the difference between the sample means is small enough to be attributed to sampling error or high enough to conclude that the population means are different.

Step-by-step solution

Given Information

Given In the question that a hypothesis test is performed to compare two population means. we have to know the sampling distribution of the difference between two sample means in order to perform a hypothesis test to compare two population means.

Explanation

A concept that can be tested is known as a hypothesis. To test the hypothesis, many statistical models are used.

The term "generally accepted fact" is used to describe a null hypothesis. The null hypotheses are being challenged, disproved, and nullified by researchers. The researcher offers an alternative hypothesis to refute the null hypothesis.

Assume that ${\mu }_1$is the mean of a variable in population 1, and ${\mu }_2$is the mean of a variable in population 2. The sampling distribution of the difference between two means is designated${\mu }_1-{\mu }_2$in this case.

This ${\mu }_1-{\mu }_2$allows researchers to assess if the difference between the sample means is small enough to be attributed to sampling error or high enough to conclude that the population means are different.

As a result, while running a hypothesis test to compare two population means, it's critical to understand the sampling distribution of the difference between two sample means.