Ch. 7 - Estimating Parameters and Determining Sample Sizes

Triola - Elementary Statistics 14th Edition

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Triola 14th Edition

Ch. 7 - Estimating Parameters and Determining Sample Sizes

Problem 7.C.3

Chapter 7, Problem 7.C.3

Cell Phone Radiation. Listed below are amounts of cell phone radiation (W/kg) measured from randomly selected cell phones (based on data from the Federal Communications Commission). Use these values for Exercises 1–6.

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Level of Measurement What is the level of measurement of these data (nominal, ordinal, interval, ratio)? Are the original unrounded amounts of radiation continuous data or discrete data?

Verified step by step guidance

Step 1: Understand the levels of measurement. There are four levels: nominal, ordinal, interval, and ratio. Nominal involves categories without any order, ordinal involves ordered categories, interval involves ordered categories with equal intervals but no true zero, and ratio involves ordered categories with equal intervals and a true zero.

Step 2: Determine the level of measurement for the cell phone radiation data. Since the data consists of numerical values representing the amount of radiation, consider whether these values have a true zero point and whether the intervals between values are consistent.

Step 3: Recognize that the data is measured in W/kg, which is a physical quantity. This suggests that the data is at the ratio level of measurement because it has a true zero point (0 W/kg means no radiation) and the intervals between values are consistent.

Step 4: Understand the difference between continuous and discrete data. Continuous data can take any value within a range, while discrete data can only take specific values. Consider whether the radiation values can be measured to any level of precision or if they are limited to specific increments.

Step 5: Conclude that the original unrounded amounts of radiation are continuous data because they can theoretically take any value within a range, allowing for precise measurement.

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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, allowing for meaningful comparisons of magnitude.

Continuous vs. Discrete Data

Continuous data can take any value within a range and are often measured, such as height or temperature. Discrete data, on the other hand, consist of distinct, separate values, often counted, like the number of students in a class. Understanding whether data are continuous or discrete helps in selecting appropriate statistical methods and visualizations.

Understanding Radiation Measurements

Radiation measurements, such as those in W/kg for cell phones, are typically ratio data because they have a true zero point and allow for meaningful comparisons of magnitude. This means that a measurement of zero indicates no radiation, and comparisons like 'twice as much radiation' are valid. Recognizing this helps in determining the appropriate statistical analyses and interpretations.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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