Final answer:
The correct answer is A, which involves comparing the between-group variation to the within-group variation by using the ratio of systematic differences to chance variation. T-tests are used for matched pairs or independent groups under the assumption of normality and equal variances.
Step-by-step explanation:
The general idea behind all t-tests is A: comparing between variation to within variation by dividing the systematic difference between two samples, or between a sample and a population, by the chance variation within the samples. The t-test is a statistical analysis used to determine if there is a significant difference between the means of two groups, which may be related in some way or independent. The concept involves determining the ratio of the variance between groups to the variance within groups.
In hypothesis testing, especially with t-tests, we often deal with matched pairs or independent samples. Matched pairs consist of subjects that are paired in some meaningful way and the differences within each pair are analyzed. In contrast, independent groups are two samples in which the subjects are not paired or matched, but each sample is selected from their respective populations without any sort of matching.
The assumption of normality and equal variances are essential when performing t-tests or ANOVA (Analysis of Variance). When sample sizes are large, however, the requirement for normal distribution can become less stringent due to the central limit theorem.