There can be two general relationships between the two samples: they can be independent from each other, or they can be dependent. Dependent samples are also called paired samples. When conducting a two-sample test of means it's important to know whether the samples are dependent or independent, particularly because we use a different test statistic. When the samples are dependent, regardless of the sample size we have to use the t-student test statistic with d.f. = n - 1.

Let's

consider a practical example that illustrates dependent samples. Suppose we

want to compare the premium prices of Progressive Insurance and State Farm

Insurance. We want to find out which one is cheaper. Let's suppose we ask 20

people to call Progressive and State Farm to figure out their premiums for the

same coverage. The same 20 people call Progressive and State Farm. So, their 20

pairs of premiums would constitute paired data, and the two samples would be

dependent samples.

in the previous scenario, what would be the

d.f. of the t-student distribution used to calculate the test statistic and

critical value?