How does increasing the sample size affect the accuracy of the sample mean?
Understand the Problem
The question is asking about the relationship between sample size and the accuracy/reliability of the sample mean as an estimator of the population mean. Specifically, it's testing your understanding of how increasing the sample size affects how close the sample mean is likely to be to the true population mean.
Answer
As the sample size increases, the accuracy of the sample also increases.
Increasing the sample size generally increases the accuracy of the sample mean because it reduces the variability of the sample mean and provides a more precise estimate of the population parameter.
Answer for screen readers
Increasing the sample size generally increases the accuracy of the sample mean because it reduces the variability of the sample mean and provides a more precise estimate of the population parameter.
More Information
A larger sample size helps to minimize the impact of random variation and provides a more reliable representation of the population.
Tips
Confusing precision and accuracy. Accuracy refers to how close an estimate is to the true value, while precision refers to the consistency or repeatability of the estimate.
Sources
- 4.1.3 - Impact of Sample Size | STAT 200 - online.stat.psu.edu
- Why does a bigger sample size give a more accurate result? - math.stackexchange.com
- Statistics in Brief: The Importance of Sample Size in the Planning ... - pmc.ncbi.nlm.nih.gov
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