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Chapter 2: Q103 (page 117)

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 鈥渙nly 44 of the 129 schools have positive z-scores, indicating that the distribution of overall productivity is skewed to the right.鈥� Do you agree?

Short Answer

Expert verified
  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

01

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.

02

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.

03

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.

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Most popular questions from this chapter

Permeability of sandstone during weathering.Refer to the Geographical Analysis(Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercises 2.47 and 2.65 (pp. 96 and 104). Recall that slices of sandstone blocks were measured for permeability under three conditions: no exposure to any type of weathering (A), repeatedly sprayed with a 10% salt solution (B), and soaked in a 10% salt solution and dried (C).

a.Combine the mean (from Exercise 2.47) and standard deviation (from Exercise 2.65) to make a statement about where most of the permeability measurements for Group A sandstone slices will fall. Which rule did you use to make this inference and why?

b.Repeat part afor Group B sandstone slices.

c.Repeat part afor Group C sandstone slices.

d.Based on all your analyses, which type of weathering (type A, B, or C) appears to result in faster decay (i.e., higher permeability measurements)?

Parking at a university has become a problem. The university鈥檚 administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 190 students and recorded how long it took each of them to find a parking spot. The durations had a distribution that was skewed to the left. Based on this information, discuss the relationship between the mean and the median for the 190 times collected.

Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 ( p. 83). Recall that level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each of 992 senior managers at CPA firms. Numerical measures of central tendency for level of support are shown in the accompanying Minitab printout.

Descriptive Statistics: Support

Variable

Support

N

Mean

Minimum

Median

Maximum

Mode

N for mode

992

67.755

0.000

68.000

155.000

64

20

a.Locate the mean on the printout. Comment on the accuracy of the statement: 鈥淥n average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points.鈥�

b.Locate the median on the printout. Comment on the accuracy of the statement: 鈥淗alf of the 992 senior managers reported a level of support for corporate sustainability below 68 points.鈥�

c.Locate the mode on the printout. Comment on the accuracy of the statement: 鈥淢ost of the 992 senior managers reported a level of support for corporate sustainability below 64 points.鈥�

d.Based on the values of the measures of central tendency, make a statement about the type of skewness (if any) that exists in the distribution of 992 support levels. Check your answer by examining the histogram shown in Exercise 2.23.

Calculate the range, variance, and standard deviation for the following samples:

a.4, 2, 1, 0, 1

b.1, 6, 2, 2, 3, 0, 3

c.8, -2, 1, 3, 5, 4, 4, 1, 3, 3

d.0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1

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鈥檚 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.
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