Textbook Question
Determine whether the survey question is biased. If the question is biased, suggest a better wording.
How does the media influence the opinions of voters?
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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 1.1.10
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A sample statistic will not change from sample to sample.
Verified step by step guidance1
Understand the concept of a sample statistic: A sample statistic is a numerical measure calculated from a sample of data, such as the sample mean, sample variance, or sample proportion. It is used to estimate the corresponding population parameter.
Recognize the variability of sample statistics: Sample statistics can vary from sample to sample because different samples may contain different data points, even if they are drawn from the same population. This variability is known as sampling variability.
Evaluate the given statement: The statement 'A sample statistic will not change from sample to sample' is false because sample statistics are subject to sampling variability and can differ depending on the specific sample selected.
Rewrite the statement as a true statement: A true version of the statement would be 'A sample statistic can change from sample to sample due to sampling variability.'
Conclude the reasoning: Sampling variability is a fundamental concept in statistics, and understanding it is crucial for interpreting sample statistics and making inferences about the population.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sample Statistic
A sample statistic is a numerical value calculated from a sample of data, which is used to estimate a population parameter. It can include measures such as the sample mean, median, or standard deviation. Since different samples can yield different values, sample statistics are inherently variable and can change from one sample to another.
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Sampling Distribution of Sample Proportion
Sampling Variability
Sampling variability refers to the natural variation that occurs when different samples are taken from the same population. Each sample may produce different statistics due to random chance, leading to different estimates of the population parameters. Understanding this concept is crucial for interpreting the results of statistical analyses and for making inferences about the population.
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05:11Sampling Distribution of Sample Proportion
True Statement Revision
When a statement is found to be false, it is important to revise it to reflect the correct understanding. In this case, the false statement can be rewritten to indicate that a sample statistic can change from sample to sample, highlighting the concept of sampling variability. This revision helps clarify the nature of statistical estimates and their dependence on the specific samples drawn.
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Guided course
06:21Step 1: Write Hypotheses
Related Practice
Textbook Question
Volunteers for an experiment are numbered from 1 to 90. The volunteers are to be randomly assigned to two different treatment groups. Use a random number generator different from the one you used in Exercise 21 to choose 45 subjects for the treatment group. The other 45 subjects will go into the control group. List the subjects, according to number, in each group. Tell which method you used to generate the random numbers.
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Textbook Question
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
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Textbook Question
A study showed an association between intentional weight loss and a decreased risk of high blood pressure. Is it appropriate to infer from this study that weight loss causes a decreased risk of high blood pressure? Explain. (Source: European Association for the Study of Obesity)
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Textbook Question
"Identify the population and the sample. Describe the sample data set.
A survey of 1500 U.S. adults found that 59% have never had a vaccine reaction. (Source: SingleCare)"
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Textbook Question
Determine whether the data are qualitative or quantitative. Explain your reasoning.
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