Question

Thousands of students apply for admission to graduate schools in economics each year with the intention of obtaining a PhD. The Southern Economic Journal (April 2008) published a guide to graduate study in economics by ranking the PhD programs at 129 colleges and universities. Each program was evaluated according to the number of publications published by faculty teaching in the PhD program and by the quality of the publications. Data obtained from the Social Science Citation Index (SSCI) were used to calculate an overall productivity score for each PhD program. The mean and standard deviation of these 129 productivity scores were then used to compute a z-score for each economics program. Harvard University had the highest z-score 1z = 5.082 and, hence, was the top-ranked school; Howard University was ranked last because it had the lowest z-score 1z = -0.812. The data (z-scores) for all 129 economic programs are saved in the data file.

a. Interpret the z-score for Harvard University.

b. Interpret the z-score for Howard University.

c. The authors of the Southern Economic Journal article note that “only 44 of the 129 schools have positive z-scores, indicating that the distribution of overall productivity is skewed to the right.” Do you agree?

Short answer

1. A total of 5.082 standard deviations are above the mean score.
2. A total of 0.812 standard deviations are below the mean score.
3. Yes.

Step-by-step solution

Interpretation of the z-score of Harvard University

The Southern Economic Journal has found the z-score associated with Harvard University is 5.082. This indicates that around 5.082 standard deviations are above the mean score of Harvard University.

Step 2:Interpretation of the z-score of Howard University

The Southern Economic Journal has found the z-score associated with Howard University is -0.812. This indicates that around 0.812 standard deviations are above the mean score of Harvard University.

Specification of skewness

The motion of the asseveration is correct that the distribution will be skewed to the right. It is because only a few schools have positive z-scores whereas a maximum number of schools have negative z-scores.

$\begin{array}{rcl}\mathit{p}\mathbf{+}\mathit{q}& \mathbf{=}& \mathbf{1}\\ \mathit{q}& \mathbf{=}& \mathbf{1}\mathbf{-}\mathit{p}\end{array}$