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Ch. 1 - Introduction to Statistics
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 1 - Introduction to StatisticsProblem 1.2.24
Chapter 1, Problem 1.2.24

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.
Criminology In a criminology study, the lengths of prison sentences are obtained for randomly selected subjects convicted of auto theft.

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Understand the four levels of measurement: Nominal, Ordinal, Interval, and Ratio. Nominal involves categories without a specific order, Ordinal involves categories with a specific order, Interval involves ordered categories with equal intervals but no true zero, and Ratio involves ordered categories with equal intervals and a true zero.
Identify the type of data you have. In this case, the data consists of the lengths of prison sentences.
Consider whether the data has a true zero point. Since a prison sentence can be zero (indicating no time served), this suggests the presence of a true zero.
Determine if the data can be ordered and if the differences between data points are meaningful. Prison sentences can be ordered (e.g., 1 year, 2 years) and the differences between them are meaningful (e.g., the difference between 1 year and 2 years is the same as between 2 years and 3 years).
Conclude that the data is best described by the ratio level of measurement, as it has a true zero, can be ordered, and the differences between values are meaningful.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Levels of Measurement

The levels of measurement refer to the different ways data can be categorized and quantified. They include nominal (categorical data without order), ordinal (categorical data with a defined order), interval (numerical data without a true zero), and ratio (numerical data with a true zero). Understanding these levels is crucial for selecting appropriate statistical methods and interpreting data correctly.
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Nominal and Ordinal Data

Nominal data represents categories without any inherent order, such as types of crimes, while ordinal data involves categories with a meaningful sequence, like rankings. In the context of prison sentences, these types are less relevant since we are dealing with numerical values rather than categories. However, recognizing these distinctions helps in understanding how to classify different types of data.
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Interval and Ratio Data

Interval data is numerical and has equal intervals between values but lacks a true zero point, such as temperature in Celsius. Ratio data, on the other hand, is also numerical but includes a true zero, allowing for meaningful comparisons of magnitude, such as lengths of prison sentences. Since prison sentences can be zero (no sentence) and have meaningful ratios, they are classified as ratio data.
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Related Practice
Textbook Question

Directions in Degrees Standard navigation systems used for aviation and boating are based on directions measured in degrees, with north represented by 0° Relative to north, east is 90°, south is 180°, and west is 270°. What is the level of measurement of such directions measured in degrees?

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Textbook Question

In Exercises 21–28, determine whether the study is an experiment or an observational study, and then identify a major problem with the study.

Sleep Study When designing the study of a new treatment for insomnia in adults, researchers were criticized because their test subjects consisted of 75 college students. They then expanded the study so that 750 college students were given the treatment.

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Textbook Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Percentages in Advertising An ad for Big Skinny wallets included the statement that one of their wallets “reduces your filled wallet size by 50%–200%.” What is wrong with this statement?

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Textbook Question

In Exercises 13–20, determine whether the results appear to have statistical significance, and also determine whether the results appear to have practical significance.


Bias in Jury Selection In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry.

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Textbook Question

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Context of the Data Refer to the table of body temperatures. Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM temperature?

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Textbook Question

In Exercises 21–24, refer to the sample of body temperatures (degrees Fahrenheit) in the table below. (The body temperatures are from Data Set 5 in Appendix B.)

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Conclusion If we analyze the listed body temperatures with suitable methods of statistics, we conclude that when the differences are found between the 8 AM body temperatures and the 12 AM body temperatures, there is a 64% chance that the differences can be explained by random results obtained from populations that have the same 8 AM and 12 AM body temperatures. What should we conclude about the statistical significance of those differences?

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