The accuracy with which a sample mean estimates a population mean rises when:
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Answer: D. the standard deviation of the sample decreases
Explanation
Decreasing sample standard deviation reduces sampling error, increasing the accuracy of sample estimates. Lower variability among sample observations means the sample mean is a more reliable population estimate. Statistical precision improves as data clustering around the mean becomes tighter and more consistent. Inferential statistics use sample data to make reliable generalizations about broader target populations. The standard error of the mean decreases when sample standard deviation decreases or sample size increases. Central limit theorem ensures that sampling distributions approximate normal curves under favorable conditions.
Researchers strive to reduce experimental variability to obtain more precise statistical estimates in studies. Quality control engineers monitor standard deviation to ensure manufacturing processes meet precise specifications. Interpreting confidence intervals requires understanding how sample variability affects population mean estimates. Increasing sample range expands data spread, which typically increases uncertainty rather than estimation accuracy. Increasing sample standard deviation widens dispersion, decreasing the precision of population mean estimates. Raising the sample mean mathematically shifts the distribution without inherently reducing estimation error.
- Subject
- Psychology
- Category
- Psychology
- Topic
- —
- Difficulty
- medium
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