Two high school students took equivalent language tests, one in German and one in French. The student taking the German test, for which the mean was 66 and the standard deviation was 8, scored an 82, while the student
Taking the French test, for which the mean was 27 and the standard deviation was 5, scored a 35. Compare the
Scores.
A)A score of 82 with a mean of 66 and a standard deviation of 8 is better.
B)A score of 35 with a mean of 27 and a standard deviation of 5 is better.
C)The two scores are statistically the same.
D)You cannot determine which score is better from the given information.

Question

Quizplus · Accepted Answer

The student taking the German test scored 1.5 standard deviations above the mean, while the student taking the French test scored 1.6 standard deviations above the mean. However, since the standard deviation for the German test was larger, scoring 1.5 standard deviations above the mean is a more impressive feat than scoring 1.6 standard deviations above the mean on the French test. Therefore, a score of 82 with a mean of 66 and a standard deviation of 8 is better. To compare the scores, we need to use z-scores, which tell us how many standard deviations above or below the mean a particular score is.

For the German test: 
z-score = (82 - 66) / 8 = 2

For the French test: 
z-score = (35 - 27) / 5 = 1.6

A z-score of 2 indicates that the score of 82 is two standard deviations above the mean for the German test, while a z-score of 1.6 indicates that the score of 35 is 1.6 standard deviations above the mean for the French test. Since a z-score of 2 is higher than a z-score of 1.6, we can conclude that the score of 82 on the German test is better than the score of 35 on the French test. Therefore, choice A is the best answer.

Two High School Students Took Equivalent Language Tests, One in German