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 1.2.21

Chapter 1, Problem 1.2.21

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.
College Students In order to better plan for the incoming freshman class, a college dean asks each newly admitted student to identify their likely major (physics, business, math, psychology, engineering, law, etc.).

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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 numerical scales with equal intervals but no true zero, and Ratio involves numerical scales with a true zero.

Identify the type of data being collected. In this case, the data consists of categories of college majors such as physics, business, math, etc.

Determine if there is any inherent order to the categories. College majors do not have a natural order; one major is not inherently 'higher' or 'lower' than another.

Since the data consists of categories without a specific order, it fits the definition of the nominal level of measurement.

Conclude that the level of measurement for the given data (college majors) is nominal, as it involves categorizing students into groups without any ranking or order.

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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, ordinal, interval, and ratio scales. Each level has distinct characteristics that determine how data can be analyzed and interpreted, influencing the types of statistical tests that can be applied.

Nominal Scale

The nominal scale is the simplest level of measurement, used for categorizing data without any order or ranking. In this scale, data is classified into distinct categories that are mutually exclusive, such as names of majors (e.g., physics, business). The only permissible operation is counting the frequency of each category.

Ordinal Scale

The ordinal scale involves categorizing data into ordered categories, where the order matters but the differences between the categories are not quantifiable. For example, if students were ranked by their preference for majors, the order would indicate preference but not the degree of difference between them. This scale allows for comparisons in terms of greater or lesser but not precise measurements.

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Textbook Question

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

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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.

Drinking and Driving A researcher for a consortium of insurance companies plans to test for the effects of drinking on driving ability by randomly selecting 1000 drivers and then randomly assigning them to two groups: One group of 500 will drive in New York City after no alcohol consumption, and the second group will drive in New York City after consuming three shots of Jim Beam bourbon whiskey.

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Textbook Question

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

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a. Among the respondents, 42% said that they text while driving. What is the exact value that is 42% of the number of respondents?

b. Could the result from part (a) be the actual number of respondents who said that they text while driving? Why or why not?

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Textbook Question

Exercises 5–8 refer to the study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed. The study is reported in “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery, Vol. 139, No. 5. The study began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.)

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Textbook Question

In Exercises 5–12, identify whether the given value is a statistic or a parameter.

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