Question
The standard error of a sample mean decreases as which of the following increases? Sample size Sample standard deviation Population size Population standard deviation
Ask by Bolton Reese. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The standard error of a sample mean decreases as the sample size increases.
Solution
The standard error of a sample mean (SE) is calculated using the formula:
\[
SE = \frac{s}{\sqrt{n}}
\]
where:
- \(s\) is the sample standard deviation,
- \(n\) is the sample size.
From this formula, we can see that the standard error decreases as the sample size (\(n\)) increases.
Now, let's analyze the options:
1. **Sample size**: As \(n\) increases, \(SE\) decreases.
2. **Sample standard deviation**: If \(s\) increases, \(SE\) increases.
3. **Population size**: The population size does not directly affect the standard error of the sample mean.
4. **Population standard deviation**: This is not directly used in the calculation of the standard error for a sample mean.
Thus, the correct answer is:
**Sample size**.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
The standard error of a sample mean decreases as the sample size increases. This happens because a larger sample gives a more accurate estimate of the population mean, thus reducing the variability of the sample mean. Think of it like rolling a dice; the more times you roll, the closer your average result gets to the true expected value! On the other hand, the sample standard deviation influences the standard error directly. If your sample standard deviation gets smaller, the standard error also shrinks, but increasing the sample size remains the most effective method to achieve a more precise estimate of the population mean. So, go for that bigger sample!
