Final answer:
To compare the GPAs between two independent groups of high-school students, those who are in sports and those who are not, after collecting the data, a two-sample t-test should be used to determine if there is a significant difference in their mean GPAs.
Step-by-step explanation:
To compare the GPAs between high-school students who participate in sports and those who do not, after gathering the data, you should apply a two-sample t-test.
This test is appropriate because you have two independent samples from the two groups and are interested in comparing their means.
It's assumed that the two groups are from a normally distributed population, which is a common assumption for a t-test.
In applying the two-sample t-test, you would establish null and alternative hypotheses, calculate the test statistic (t-score), and compare it with the critical t-value from the t-distribution tables (or use a p-value approach) based on the desired significance level.
The two-sample t-test will determine if there is a statistically significant difference between the mean GPAs of students who participate in sports and those who do not.