Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.

A. The above statement is incorrect, the sample size has no effect on the sampling error.
B. The larger the sample size, the more closely the possible values of \bar{x} cluster around the mean of \bar{x}
C. If the sample size is larger, the possible values of \bar{x} are farther from the mean of \bar{x},

B is the correct answer. The more values or samples you are able to add, the closer you come to approximating real life (although that is impossible) because you are more likely to have a cluster of values around the mean.

Answer Link

jainveenamrata jainveenamrata · Answer 2 · 2022-04-06T12:22:08+02:00

Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases. Then option B is correct.

What is sampling error?

The amount of inaccuracy in the estimating value appears due to the smaller sample size.

The sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.

We know that the formula of the sampling error

[tex]\rm Sampling \ error = z \times \dfrac{\sigma}{\sqrt{n}}[/tex]

Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases.

More about the sampling error link is given below.

https://brainly.com/question/15375591