Final answer:
The t-test is used to test for a significant difference between the means of two samples, and it falls under inferential statistics aimed at testing hypotheses. The t-test can be used for comparing two independent means, the mean differences in matched pairs, or a single mean against a known value or standard.
Step-by-step explanation:
The researcher understands that the t-test is used to C. Test for a significant difference between the means of two samples. The t-test is a form of inferential statistics that is designed to test hypotheses about the population mean or means. The t-test can serve different purposes including:
b. a test of two independent means: This is used when comparing the means from two separate groups to see if they significantly differ from one another.d. a test of matched pairs: In this scenario, subjects are paired, and their differences are used to conduct the test, focusing on determining if the mean difference is significantly different from zero.c. a test of a single mean: This is applied when testing against a known value or a standard.
The t-test can be used as an Aspin-Welch t-test if the two samples' population standard deviations are unknown and possibly unequal, which affects the calculation of degrees of freedom for the t-test.
Overall, inferential statistics like the t-test help determine whether the observed data could occur by chance or indicate a meaningful difference that supports the hypothesis being tested. This relates to the concept of the hypothesis test, which uses statistical methods to decide if observed results significantly deviate from what is expected under the null hypothesis.