1. The one-sample case versus the two-sample case

In the one-sample case, you are comparing the statistic from a sample to a known population parameter to determine whether the sample is from the general population. In the two-sample case, you are comparing the statistics from two different samples to determine whether the samples are from the same or different populations. There are important differences between the one-sample case and the two-sample case.

Suppose you wish to test whether the mean SAT score of students who took an intensive SAT preparation course is the same as the national average SAT score. Will this consist of a one-sample or a two-sample hypothesis test?

Two-sample

Neither

One-sample

The two-sample case requires the assumption that there is independent random sampling. Suppose you wish to investigate whether participation in intensive SAT preparation courses affects SAT scores. You select a random sample of 78 students and obtain their SAT scores. Are both samples independent random samples?

No

Yes

Not applicable

Can you use the sample or samples you collected to conduct the hypothesis test you will use to investigate your research question?

No

Yes

Not applicable