Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

1. Intro to Stats and Collecting Data

Intro to Stats

Statistics

1. Intro to Stats and Collecting Data

Intro to Stats

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3:06 minutes

Problem 1.2.27

Textbook Question

In Exercises 21–28, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) best describes the given data.
Areas of States A data set consists of the areas of each of the 50 United States.

Verified step by step guidance

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 data without a true zero, and Ratio involves numerical data with a true zero.

Identify the type of data you have. In this case, the data set consists of the areas of each of the 50 United States.

Consider whether the data has a true zero point. Since area can be zero (a state could theoretically have no area), this suggests a true zero exists.

Determine if the data can be compared using multiplication or division. Since you can say one state is twice as large as another, this supports the presence of a ratio level of measurement.

Conclude that the areas of the states are best described by the ratio level of measurement, as they have a true zero and allow for meaningful comparisons using multiplication and division.

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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 in which data can be categorized and quantified. There are four primary levels: nominal (categorical data without a specific order), ordinal (categorical data with a defined order), interval (numerical data with equal intervals but no true zero), and ratio (numerical data with equal intervals and a true zero). Understanding these levels is crucial for correctly analyzing and interpreting data.

Nominal Measurement

Nominal measurement is the simplest level of measurement, where data is categorized without any order or ranking. Examples include gender, race, or types of fruit. In the context of the question, nominal measurement would not apply to the areas of states, as these can be quantitatively compared.

Ratio Measurement

Ratio measurement is the highest level of measurement, characterized by the presence of a true zero point and the ability to perform meaningful mathematical operations. In this level, both differences and ratios are meaningful, allowing for comparisons such as 'twice as large.' The areas of states fit this category, as they can be measured in square miles, allowing for direct comparisons and calculations.

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