Chapter 2: Q92. (page 116)
In terms of percentiles, define QL, QM and QU
The QL is 25th percentile.
The QM is 50th percentile.
The QU is 75th percentile.
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Improving SAT scores.The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the Standardized Assessment Test (SAT) scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the changes in both the SAT–Mathematics and SAT–Verbal scores for these students.
SAT–Math | SAT–Verbal | |
Mean change in score | 19 | 7 |
Standard deviation of score changes | 65 | 49 |
a.Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain this student’s change in the SAT–Math score.
b.Repeat part afor the SAT–Verbal score.
c.Suppose the selected student increased his score on one of the SAT tests by 140 points. Which test, the SAT– Math or SAT–Verbal, is the one most likely to have the 140-point increase? Explain.
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 |
Microsoft program security issues. To help its users combat malicious attacks (e.g., worms, viruses) on its computer software, Microsoft periodically issues a security bulletin that reports the software affected by the vulnerability. In Computers & Security (July 2013), researchers focused on reported security issues with three Microsoft products: Office, Windows, and Explorer
a. In a sample of 50 security bulletins issued in a recent year, 32 reported a security issue with Windows, 6 with Explorer, and 12 with Office. Construct a pie chart to describe the Microsoft products with security issues. Which product had the lowest proportion of security issues?
b. The researchers also categorized the security bulletins according to the expected repercussion of the vulnerability. Categories were Denial of service, Information disclosure, Remote code execution, Spoofing, and Privilege elevation. Suppose that of the 50 bulletins sampled, the following numbers of bulletins were classified into each respective category: 6, 8, 22, 3, 11. Construct a Pareto diagram to describe the expected repercussions from security issues. Based on the graph, what repercussion would you advise Microsoft to focus on?
Calculate the mode, mean, and median of the following data:
18 10 15 13 17 15 12 15 18 16 11
Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.
a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?
b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
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