Final answer:
When comparing multiple population means, conducting multiple two-sample t-tests increases the chance of a Type I error. ANOVA is the preferred method as it controls for the overall error rate and is designed for comparing the means of three or more groups.Option A is the correct answer.
Step-by-step explanation:
When comparing several population means, performing multiple two-sample t-tests is not advisable because it would substantially increase the chance of getting at least one Type I error.
This phenomenon is known as the "error rate inflation." As you conduct more tests, the likelihood of mistakenly rejecting the null hypothesis when it is true increases. This is because each test is conducted at a certain significance level, commonly 0.05, so the more tests you run, the greater the total probability of encountering at least one spurious significant result.
Instead of conducting multiple two-sample t-tests, a more appropriate statistical method such as Analysis of Variance (ANOVA) is used. ANOVA is designed to test differences between three or more group means while controlling the overall Type I error rate.
It does this by comparing the variation within each group to the variation between the groups. If there is significant variation between the groups compared to within the groups, ANOVA can help determine that at least one group mean is different. To perform ANOVA, certain assumptions must be met, including that each population is normally distributed, that populations have equal standard deviations (or variances), and that the response is a numerical value.