Textbook Question
Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain.
The average distance traveled to a stadium by 55,000 spectators
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1. Intro to Stats and Collecting Data
Intro to Stats
1:42 minutesProblem 1.RE.6
Textbook Question
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.
In a survey of 1000 household food purchasers, 24.7% say that they avoid meat, dairy, and eggs produced by animals living in confined conditions. (Source: FoodPrint)
Verified step by step guidance1
Identify the key terms in the problem: A population parameter refers to a numerical value that describes a characteristic of an entire population, while a sample statistic refers to a numerical value that describes a characteristic of a subset (sample) of the population.
Examine the context of the problem: The problem mentions a survey of 1000 household food purchasers. This indicates that the data was collected from a subset of the entire population of household food purchasers.
Determine whether the percentage provided (24.7%) is based on the entire population or just the sample: Since the survey was conducted on 1000 individuals, this percentage represents a characteristic of the sample, not the entire population.
Conclude that the number 24.7% is a sample statistic because it is derived from a subset of the population (the 1000 surveyed individuals) rather than the entire population of household food purchasers.
Explain the reasoning: A sample statistic is used to estimate or infer information about the population parameter. In this case, the 24.7% is an estimate of the proportion of all household food purchasers who avoid meat, dairy, and eggs produced by animals in confined conditions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Population Parameter
A population parameter is a numerical value that summarizes a characteristic of an entire population. It is a fixed value that is often unknown and can only be estimated through sampling. In the context of the question, if the percentage of 24.7% were derived from the entire population of household food purchasers, it would be considered a population parameter.
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Parameters vs. Statistics
Sample Statistic
A sample statistic is a numerical value that summarizes a characteristic of a sample drawn from a population. It is used to estimate the corresponding population parameter. In this case, the 24.7% figure comes from a survey of 1000 households, making it a sample statistic that reflects the behavior of a subset of the larger population of all household food purchasers.
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Sampling Methodology
Sampling methodology refers to the techniques used to select individuals from a population to participate in a study. The validity of a sample statistic depends on how representative the sample is of the population. Understanding the sampling method used in the survey is crucial for assessing the reliability of the 24.7% statistic and determining whether it can be generalized to the entire population.
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