Answer :
Answer:
d. All of these choices are true.
Step-by-step explanation:
The standard error of the sample mean is given by the following formula:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and [tex]n[/tex] is the size of the sample.
a. is never larger than the standard deviation of the population
We have that [tex]n \geq 1[/tex]. This means that, yes, the standard error of the sample mean is never larger than the standard deviation of the population.
b. decreases as the sample size increases.
As the sample size increases, [tex]n[/tex] increases. This means that [tex]s[/tex] decreases. So this is also correct.
c. measures the variability of the mean from sample to sample.
This is the definition of the standard error of the sample mean, so it is true.
The correct answer is
d. All of these choices are true.