Question
Which of the following statements is true regarding the standard error of the mean?(1 point)
Responses
It decreases as the sample size increases.
It decreases as the sample size increases.
It is always greater than the population standard deviation.
It is always greater than the population standard deviation.
It measures the variability of the sample means around the population mean.
It measures the variability of the sample means around the population mean.
It is equal to the population standard deviation divided by the sample size.
Responses
It decreases as the sample size increases.
It decreases as the sample size increases.
It is always greater than the population standard deviation.
It is always greater than the population standard deviation.
It measures the variability of the sample means around the population mean.
It measures the variability of the sample means around the population mean.
It is equal to the population standard deviation divided by the sample size.
Answers
GPT-4o mini
The true statement regarding the standard error of the mean is:
**It measures the variability of the sample means around the population mean.**
Additionally, it is worth noting that the standard error of the mean (SEM) is indeed calculated as the population standard deviation divided by the square root of the sample size, which can be expressed as:
\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]
where \(\sigma\) is the population standard deviation and \(n\) is the sample size. Therefore, the specific statement "It is equal to the population standard deviation divided by the sample size" is incorrect; it's divided by the square root of the sample size, not just the sample size. The first statement is also correct ("It decreases as the sample size increases"), but the most accurate regarding the definition and function of the standard error is the one about variability around the population mean.
**It measures the variability of the sample means around the population mean.**
Additionally, it is worth noting that the standard error of the mean (SEM) is indeed calculated as the population standard deviation divided by the square root of the sample size, which can be expressed as:
\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]
where \(\sigma\) is the population standard deviation and \(n\) is the sample size. Therefore, the specific statement "It is equal to the population standard deviation divided by the sample size" is incorrect; it's divided by the square root of the sample size, not just the sample size. The first statement is also correct ("It decreases as the sample size increases"), but the most accurate regarding the definition and function of the standard error is the one about variability around the population mean.