Textbook Question
"Determine whether the data set is a population or a sample. Explain your reasoning.
A survey of 250 members from an organized union of over 20,000 members"
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Ch. 1 - Introduction to Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 1, Problem 1.CR.4
In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.
In 2021, the median annual salary of a first-year chemist was \$58,700.
Verified step by step guidance1
Understand the difference between a parameter and a statistic: A parameter is a numerical value that describes a characteristic of a population, while a statistic is a numerical value that describes a characteristic of a sample drawn from the population.
Identify the context of the given number: The problem states that the median annual salary of a first-year chemist in 2021 was \$58,700.
Determine whether the number refers to the entire population or a sample: If the number represents all first-year chemists in 2021, it is a parameter. If it represents only a subset (sample) of first-year chemists, it is a statistic.
Analyze the phrasing of the problem: The problem does not explicitly mention that the number is based on a sample, so it is reasonable to assume it refers to the entire population of first-year chemists in 2021.
Conclude: Since the number likely represents the entire population, it is a parameter. If additional information were provided indicating it was based on a sample, it would instead be a statistic.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Parameter
A parameter is a numerical value that summarizes a characteristic of a population. It is a fixed value that is usually unknown and can only be estimated through sample data. In the context of statistics, parameters are often denoted by Greek letters, such as μ for the population mean or σ for the population standard deviation.
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Parameters vs. Statistics
Statistic
A statistic is a numerical value that summarizes a characteristic of a sample drawn from a population. Unlike parameters, statistics can vary depending on the sample selected and are used to estimate population parameters. Common examples include sample means (x̄) and sample proportions (p̂), which help infer characteristics about the larger population.
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Median
The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers. It is particularly useful for understanding the distribution of salaries, as it is less affected by extreme values than the mean.
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Related Practice
Textbook Question
In Exercises 9 and 10, determine whether the study is an observational study or an experiment. Explain.
To study the effect of using digital devices in the classroom on exam performance, researchers divided 726 undergraduate students into three groups, including a group that was allowed to use digital devices, a group that had restricted access to tablets, and a control group that was “technologyfree.” (Source: Massachusetts Institute of Technology)
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Textbook Question
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
More types of calculations can be performed with data at the nominal level than with data at the interval level.
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Textbook Question
Identify the sampling technique used in each study. Explain your reasoning.
A study on attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed.
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Textbook Question
Determine whether the study is an observational study or an experiment. Explain.
Researchers conduct a study to determine whether cataract surgery patients experience different comfort levels during their first and second surgeries. Researchers based their results on a verbal questionnaire. (Source: Medicine)
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Textbook Question
In Exercises 11 and 12, determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set.
The six top-earning states in 2019 by median household income are listed. (Source: U.S. Census Bureau)
1. Maryland 2. New Jersey 3. Hawaii
4. Massachusetts 5. Connecticut 6. Alaska
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