Question

Blue- vs. red-colored exam study. In a study of how external clues influence performance, university professors gave two different forms of a midterm examination to a large group of introductory students. The questions on the exam were identical and in the same order, but one exam was printed on blue paper and the other on red paper (Teaching Psychology, May 1998). Grading only the difficult questions on the exam, the researchers found that scores on the blue exam had a distribution with a mean of 53% and a standard deviation of 15%, while scores on the red exam had a distribution with a mean of 39% and a standard deviation of 12%. (Assume that both distributions are approximately mound-shaped and symmetric.)

a. Give an interpretation of the standard deviation for the students who took the blue exam.

b. Give an interpretation of the standard deviation for the students who took the red exam.

c. Suppose a student is selected at random from the group of students who participated in the study and the student’s score on the difficult questions is 20%. Which exam form is the student more likely to have taken, the blue or the red exam? Explain.

Short answer

1. The scores can fluctuate by 15 percent from the mean.
2. The scores can fluctuate by 12 percent from the mean.
3. Red exam.

Step-by-step solution

Elucidating the standard deviation of the scores on the blue exam.

The standard deviation of the scores scored by the students giving the blue exam indicates how the scores vary from the mean scores.The scores vary by about 15 percent from the mean of 53 percent.

Explaining the standard deviation of the scores on the red exam.

The standard deviation of the scores scored by the students giving the red exam indicates how the scores vary from the mean scores.The scores vary by about 15 percent from the mean of 39 percent.

Specifying the form of exam likely to be given by the students

The calculations of the z-score, which would have resulted from giving the blue and red exams, are shown below:

$$\begin{gathered} \text{z} \left(\text{Blue} \text{exam}\right)\text{=}\frac{\text{Student's} \text{score on the difficulty questions - Mean score}}{\text{Standard deviation}} \\ \text{=}\frac{\text{20 - 53}}{\text{15}} \\ \text{= - 2.20} \\ \text{z}\left(\text{Red} \text{exam}\right)\text{=}\frac{\text{Student's} \text{score on the difficulty questions - Mean score}}{\text{Standard deviation}} \\ \text{=}\frac{\text{20 - 39}}{\text{12}} \\ \text{= - 1.58} \end{gathered}$$

Since the z-score of the red exam is closer to zero compared to that of the blue exam, the students will prefer to give the red exam instead of the blue exam.