When comparing two z scores to assess performance on an exam, one would conclude that a student with a z of -2.7 outperformed someone with a z of 1.3 because the first score is more extreme.

Question

Quizplus · Accepted Answer

A z score represents the number of standard deviations a data point is from the mean. A negative z score indicates that the data point is below the mean, while a positive z score indicates that the data point is above the mean.

In this case, a z score of -2.7 indicates that the student's score was 2.7 standard deviations below the mean, while a z score of 1.3 indicates that the other student's score was 1.3 standard deviations above the mean. However, it is important to note that a higher (positive) z score does not necessarily mean better performance. It simply means that the score is further from the mean in a positive direction.

Therefore, the correct answer is B: one cannot conclude which student performed better based solely on their z scores. Additional information, such as the mean and standard deviation of the exam scores, would need to be considered.

When Comparing Two Z Scores to Assess Performance on an Exam