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Chapter 2: 131E (page 132)

Performance ratings of government agencies.The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, summer 2008). Evaluation scores ranged from 12 (lowest) to 60 (highest). The PARS evaluation scores for two consecutive years are shown in the next table.

a.Construct a scatterplot for the data. Do you detect atrend in the data?

b.Based on the graph, identify one or two agencies that hadgreater than expected PARS evaluation scores for year 2.

Short Answer

Expert verified

(a) The graph is given below:


(a) State and USAID

Step by step solution

01

Constructing the scatter plot and detecting the trend

We will plot the data for Year 1 on the x-axis and the data for Year 2 on the y-axis.

The graph is given below:

Although the data is quite varied, we can notice a general upward sloping trend.There is a positive correlation between the scores from years 1 and 2.

02

Identifying the agency with an unexpectedly high score in year 2

Based on the points in the graph, (31, 50) are in correspondence to State. In the first year, it scored 31 points, and then in year 2, it jumped to 50.Therefore,State Agency has an unexpectedly high score in year 2.

Another agency with an unexpectedly high score in year 2 is USAID,with 32 points in year 1 and 42 points in year 2.

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Most popular questions from this chapter

Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.

a.Would you consider 400 sags per week unusual, statistically? Explain.

b.Would you consider 100 swells per week unusual, statistically? Explain.

The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: \(400, \)350, \(600, \)525, and $450. Calculate each of the following values for this data:

a.The sample mean

b.The sample median

c.The sample range

d.The standard deviation

Nuclear power plants.According to the Nuclear Energy Institute (NEI), 62 nuclear power plants were operating in the United States in 2015. The table at top of the next column lists the 30 states that operate nuclear power

plants, the number of plants in each state, and whether the state has passed legislation supporting nuclear energy expansion (regulated) or not (deregulated).

a.Find the mean, median, and mode of the number of power plants per state. Interpret these values.

b.Repeat part afor the regulated states only.

c.Repeat part afor the deregulated states only.

d.Compare the results, parts band c.What inference can you make about the impact that state regulation has on the number of nuclear power plants?

e.Eliminate the state with the largest number of power plants from the data set and repeat part a.What effect does dropping this measurement have on the measures of central tendency found in part a?

f.Arrange the 30 values in the table from lowest to highest. Next, eliminate the lowest two values and the highest two values from the data set and find the mean of the remaining data values. The result is called a 10% trimmed meanbecause it is calculated after removing the highest 10% and the lowest 10% of the data values. What advantages does a trimmed mean have over the regular arithmetic mean?

State

Status

Number of Power Plants

Alabama

Regulated

2

Arizona

Regulated

1

Arkansas

Regulated

1

California

Regulated

1

Connecticut

Deregulated

1

Florida

Regulated

3

Georgia

Regulated

2

Illinois

Deregulated

6

Iowa

Deregulated

1

Kansas

Regulated

1

Louisiana

Regulated

2

Maryland

Deregulated

1

Massachusetts

Deregulated

1

Michigan

Deregulated

3

Minnesota

Regulated

2

Mississippi

Regulated

1

Missouri

Regulated

1

Nebraska

Regulated

2

New Hampshire

Deregulated

1

New Jersey

Deregulated

3

New York

Deregulated

4

North Carolina

Regulated

3

Ohio

Deregulated

2

Pennsylvania

Deregulated

5

South Carolina

Regulated

4

Tennessee

Regulated

2

Texas

Deregulated

2

Virginia

Regulated

2

Washington

Regulated

1

Wisconsin

Deregulated

1

Professional athletes’ salaries.The salaries of superstar professional athletes receive much attention in the media. The multimillion-dollar long-term contract is now commonplace among this elite group. Nevertheless, rarely does a season pass without negotiations between one or more of the players’ associations and team owners for additional salary and fringe benefits for allplayers in their particular sports.

a.If a players’ association wanted to support its argument for higher “average” salaries, which measure of central tendency do you think it should use? Why?

b.To refute the argument, which measure of central tendency should the owners apply to the players’ salaries? Why?

Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.
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