Ch. 1 - Introduction to Statistics

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 1 - Introduction to Statistics

Problem 1.CQQ.2

Chapter 1, Problem 1.CQQ.2

Survey Which of the following best describes the level of measurement of the numbers 1, 2, 3, . . . , 410 described in Exercise 1: nominal, ordinal, interval, ratio?

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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 context in which the numbers 1, 2, 3, ..., 410 are used. This context will help determine the level of measurement.

Consider if the numbers represent categories without order (nominal) or with order (ordinal). If they represent a ranking or position, they might be ordinal.

Determine if the numbers have meaningful intervals between them (interval level) or if they have a true zero point, which would indicate a ratio level of measurement.

Conclude the level of measurement by matching the characteristics of the numbers to the definitions of nominal, ordinal, interval, or ratio. For example, if the numbers represent a count with a true zero, they are at the ratio level.

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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 nature of data and dictate the types of statistical analyses that can be performed. The four levels are nominal, ordinal, interval, and ratio. Nominal data categorize without a specific order, ordinal data have a defined order, interval data have equal intervals without a true zero, and ratio data have equal intervals with a true zero.

Ordinal Level

The ordinal level of measurement involves data that can be ordered or ranked, but the differences between data points are not meaningful. For example, survey responses like 'satisfied,' 'neutral,' and 'dissatisfied' can be ranked, but the difference between them is not quantifiable. This level is crucial for understanding data that imply a sequence or order.

Interval and Ratio Levels

Interval and ratio levels of measurement both involve numerical data with meaningful differences between values. Interval data lack a true zero point, such as temperature in Celsius, while ratio data have a true zero, allowing for meaningful ratios, such as weight or height. Understanding these distinctions helps in selecting appropriate statistical methods for analysis.

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Related Practice

Textbook Question

In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation.

(0.2)^12

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Textbook Question

Physicians’ Health Study In the Physicians’ Health Study, some of the subjects were treated with aspirin while others were given a placebo. For the subjects in this experiment, what is blinding?

(8)^12

Birth Weights For 100 randomly selected births from Bellevue Hospital Center, the birth weights are added and then divided by 100. The result is 3240 g. Is the value of 3240 g a statistic or a parameter?

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Textbook Question

Types of Data In each of the following, identify the level of measurement of the sample data (nominal, ordinal, interval, ratio) and the type of sampling used to obtain the data (random, systematic, convenience, stratified, cluster).

b. In each of the 50 states, 50 voters are randomly selected and their political party affiliations are identified.

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Textbook Question

Birth Weights Refer to the sample described in Exercise 6. Because Bellevue Hospital Center agreed to provide the 100 birth weights, does the sample of birth weights constitute a voluntary response sample?

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