Textbook Question
Determine whether each number describes a population parameter or a sample statistic. Explain.
In a recent year, the average evidence-based reading and writing score on the SAT was 528. (Source: College Board)
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Ch. 1 - Introduction to Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 1, Problem 1.RE.18
Determine the level of measurement of the data set. Explain.
The total compensations (in millions of dollars) of the ten highest-paid CEOs at U.S. public companies are listed. (Source: 24/7 Wall St.)
280.6 66.9 42.9 36.5 34.3 31.6 31.6 28.8 26.4 25.8
Verified step by step guidance1
Identify the four levels of measurement in statistics: nominal, ordinal, interval, and ratio. Each level represents a different way of categorizing and interpreting data.
Examine the data set provided: 280.6, 66.9, 42.9, 36.5, 34.3, 31.6, 31.6, 28.8, 26.4, 25.8. These are numerical values representing the total compensations of CEOs in millions of dollars.
Determine if the data has a true zero point. In this case, a compensation of \$0 would indicate the absence of compensation, which confirms the presence of a true zero point.
Assess whether the data can be meaningfully compared using ratios. For example, a compensation of \$280.6 million is 10 times greater than \$28.8 million, which is a valid ratio comparison. This confirms that the data is at the ratio level of measurement.
Conclude that the level of measurement for this data set is 'ratio' because it is numerical, has a true zero point, and allows for meaningful ratio comparisons.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Levels of Measurement
Levels of measurement refer to the different ways data can be categorized and quantified. There are four primary levels: nominal, ordinal, interval, and ratio. Each level has distinct characteristics, with ratio being the highest level, allowing for meaningful comparisons and calculations, including the use of absolute zero.
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Difference in Proportions: Hypothesis Tests Example 1
Ratio Level Data
Ratio level data is a type of quantitative data that possesses all the properties of interval data, but also includes a true zero point, which allows for the comparison of absolute magnitudes. In the context of the CEO compensation data, the total compensations can be compared, and a value of zero would indicate no compensation, making it a ratio level measurement.
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Descriptive Statistics
Descriptive statistics involve summarizing and organizing data to understand its main features. This includes measures such as mean, median, and mode, which can provide insights into the central tendency of the compensation figures. Understanding these statistics is essential for interpreting the data set effectively.
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05:53Parameters vs. Statistics
Related Practice
Textbook Question
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.
In a survey of 1000 household food purchasers, 24.7% say that they avoid meat, dairy, and eggs produced by animals living in confined conditions. (Source: FoodPrint)
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Textbook Question
Determine whether the data are qualitative or quantitative. Explain your reasoning.
The marital statuses of the employees of a casino
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Textbook Question
Which part of the survey described in Exercise 3 represents the descriptive branch of statistics? Make an inference based on the results of the survey.
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Textbook Question
Identify the population and the sample. Describe the sample data set.
Eighty-three doctors working in the St. Louis area were surveyed concerning their opinions on health care reform.
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Textbook Question
Determine whether the data are qualitative or quantitative. Explain your reasoning.
The zip codes of a sample of 200 customers at a sporting goods store
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