What is the difference between a sample mean and the population mean called?
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A. B. C. D. E.Explanation
This is the error incurred when sampling from a population.
The difference between a sample mean and the population mean is referred to as "sampling error." Therefore, the correct answer to the question is A. Sampling error.
To understand the concept better, let's break down the terms involved:
Population Mean: The population mean represents the average value of a variable in an entire population. It is a parameter that describes the central tendency of the population. However, calculating the population mean is often impractical or impossible due to the large size of the population or resource limitations.
Sample Mean: A sample mean is the average value of a variable calculated from a subset of the population, known as a sample. A sample is a smaller representative group selected from the population to gather data. The sample mean is an estimate of the population mean and is used to make inferences about the population.
Sampling Error: Sampling error refers to the discrepancy between the sample mean and the population mean. It occurs due to the inherent variability or chance fluctuations that arise when using a sample to estimate the characteristics of a larger population. Sampling error can be caused by random sampling, measurement errors, or other sources of variation.
When we take a sample from a population, we use the sample mean as an estimate of the population mean. However, because we are working with a subset of the population rather than the entire population, there will always be some difference or error between the sample mean and the true population mean. This difference is known as the sampling error.
Option A, "Sampling error," accurately describes this difference between the sample mean and the population mean. Option B, "Point estimate," refers to the specific value used to estimate an unknown population parameter, but it does not specifically address the difference between the sample mean and the population mean. Option C, "Standard error of the mean," represents the standard deviation of the sampling distribution of sample means, which is a measure of the precision of the sample mean estimate, but it does not directly describe the difference between the sample mean and the population mean. Option D, "None of these answers," is incorrect. Option E, "Interval estimate," refers to a range of values within which the population parameter is likely to fall, but it does not specifically address the difference between the sample mean and the population mean.