Textbook Question
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Inferential statistics involves using a population to draw a conclusion about a corresponding sample.
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1. Intro to Stats and Collecting Data
Intro to Stats
2:42 minutesProblem 1.1.18
Textbook Question
Determine whether the data set is a population or a sample. Explain your reasoning.
The amount spent by every tenth person cashing out at a store
Verified step by step guidance1
Step 1: Understand the definitions of population and sample. A population refers to the entire group of individuals or items that you want to study, while a sample is a subset of the population selected for analysis.
Step 2: Analyze the description of the data set. The problem states that the data is collected from 'every tenth person cashing out at a store.' This indicates that not all individuals cashing out at the store are included in the data set.
Step 3: Recognize that selecting 'every tenth person' is a sampling method. This approach is known as systematic sampling, where individuals are chosen at regular intervals from the population.
Step 4: Conclude that the data set represents a sample, not a population, because it does not include all individuals cashing out at the store but rather a subset of them.
Step 5: Explain the reasoning. The data set is a sample because it is derived from a systematic selection process (every tenth person), which is a subset of the larger population of all people cashing out at the store.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Population
A population refers to the entire group of individuals or items that share a common characteristic. In statistics, it encompasses all possible observations that could be made. For example, if we consider all customers who cash out at a store, that entire group constitutes the population.
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Sample
A sample is a subset of a population, selected to represent the larger group. It is used in statistical analysis to draw conclusions about the population without needing to collect data from every individual. In the context of the question, the amount spent by every tenth person is a sample of the total customer population.
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Sampling Method
The sampling method refers to the technique used to select individuals from a population to form a sample. Different methods, such as random sampling or systematic sampling, can influence the representativeness of the sample. In this case, selecting every tenth person is an example of systematic sampling, which can help ensure that the sample reflects the population's characteristics.
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