Question

Specify the differences between a large-sample and a small-sample test of a hypothesis about a population mean m. Focus on the assumptions and test statistics.

Short answer

A large-sample, as well as a small-sample hypothesis test of a population, mean, $\mu$vary because a large sample can be considered to be typically disturbed.

Step-by-step solution

Hypothesis

A hypothesis is an assumption formed based on facts. This is the first step in every inquiry that converts research issues into forecasts. It consists of variables, a population, as well as the relationship among the variables. A research hypothesis is a theory used to evaluate the link among two or more variables.

Explanation

In a population's large-sample and small-sample hypothesis tests, the mean varies because a large sample can be considered typically disturbed. As a result, one can use a normally distributed area to conduct an extensive sample hypothesis test. However, this assumption may not remain valid for a smaller sample. Therefore we utilize the t distribution for a minor sample hypothesis test.