Independent and Paired Sample t-Tests
Example 1
A researcher wanted to determine whether there are differences between men and women voters in their attitudes toward welfare.
Separate samples of men and women were drawn at random and administered an attitude scale. Women had a mean of 38.00 (on a scale from 0 to 50, where 50 was the most favorable attitude).
Men had a mean of 35.00. The researcher wanted to determine whether there is a significant difference between the two means.
What accounts for the 3-point difference between a mean of 38 and a mean of 35? One possible explanation is that the population of women has a more favorable attitude than the population of men and that the two samples correctly reflect this difference between the two populations.
Another possible explanation is raised by the null hypothesis, which states that there is no true difference between men and women that the observed difference is due to sampling errors created by random sampling.