What statistic would you need to determine if Jennifer's verbal aptitude score is significantly higher than her mathematical aptitude score?

To determine if Jennifer's verbal aptitude score is significantly higher than her mathematical aptitude score, it is essential to assess the statistical difference between the two scores. The standard error of difference is a key statistic used for this purpose. It allows for the comparison of two independent means, taking into account the variability of each score and enabling a determination of whether any observed difference is significant or likely due to random chance.

When employing the standard error of difference, you can calculate the confidence interval around the difference of the two scores. If the confidence interval does not include zero, it suggests that the difference is statistically significant, indicating that Jennifer's verbal aptitude score is indeed significantly higher than her mathematical score.

The other statistics mentioned, such as mean difference, correlation coefficient, and standard deviation, serve different purposes. While the mean difference indicates the raw difference between the two scores, it does not account for variability and does not indicate significance by itself. The correlation coefficient measures the relationship between two variables rather than comparing their significance directly. Similarly, the standard deviation describes the spread of scores within a single variable, but it does not provide insight into the difference between two distinct scores. Therefore, the standard error of difference is the most appropriate choice for evaluating significance in this context.