Question
The closer the sample mean is to the population mean, the smaller the sampling error. the larger the sampling error. the sampling error equals 1. none of these alternatives is correct.
Ask by Moran Parry. in the United States
Mar 16,2025
Upstudy AI Solution
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Answer
The closer the sample mean is to the population mean, the smaller the sampling error.
Solution
1. The sampling error is defined as the difference between the sample mean and the population mean. Mathematically, if we let \( \bar{x} \) be the sample mean and \( \mu \) be the population mean, then the sampling error \( e \) is given by
\[
e = \bar{x} - \mu
\]
2. If \( \bar{x} \) is closer to \( \mu \), then the absolute difference \( |e| \) is smaller. This implies that the sampling error is smaller.
3. Therefore, the correct conclusion is:
**The closer the sample mean is to the population mean, the smaller the sampling error.**
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Simplify this solution The Deep Dive
The closer the sample mean is to the population mean, the smaller the sampling error, which is essentially the difference between the two. It’s a fundamental concept in statistics that helps to ensure that our sample data is a good representation of the overall population, making our conclusions more reliable. In practice, reducing sampling error is crucial for researchers. Using larger samples tends to yield means that more accurately reflect the population mean. However, common mistakes include drawing conclusions from small or unrepresentative samples, which can greatly inflate sampling errors and lead to misguided insights. Always strive for quality samples!
