Question

in calculating the standard error, the population standard deviation is estimated by the sample standard deviation. the population variance. the population standard deviation. the sample variance.

Explanation:

When calculating the standard error, if the population standard deviation ($\sigma$) is unknown (which is often the case in practice), we use the sample standard deviation ($s$) as an estimator. The formula for the standard error of the mean is $SE=\frac{\sigma}{\sqrt{n}}$ when $\sigma$ is known. When $\sigma$ is unknown, we replace it with $s$ and get $SE = \frac{s}{\sqrt{n}}$. The population variance ($\sigma^{2}$) and sample variance ($s^{2}$) are measures of spread in terms of squared units and do not directly estimate the population standard deviation. Using the population standard deviation itself would be circular if we are trying to estimate it.

Answer:

the sample standard deviation.