Which of the following scenarios would a t-test be appropriate for?

The scenario that involves determining the difference in average scores between two groups is a classic application of the t-test. This statistical method is specifically designed to compare the means of two groups to see if there is a statistically significant difference between them.

In a typical t-test setup, you would have two samples—each representing a group—and you would calculate their means and the variability within each group. The t-test helps assess whether the difference between these means is greater than what could be expected due to random chance alone, thereby providing insights into whether the groups differ in a meaningful way regarding the variable being measured.

This makes the t-test a powerful tool for researchers seeking to understand how two distinct groups compare, often in experimental settings or observational studies. The other scenarios presented do not involve the comparison of means and thus would not be suitable for a t-test. For example, simply comparing frequencies (as in the first option) involves categorical data, which would typically utilize a chi-square test instead. Analyzing the relationship between two continuous datasets would be more appropriate for correlation or regression analysis. Visualizing the distribution of a single variable falls under descriptive statistics and does not involve comparisons between groups.