Question

question #3
which of the following descriptions best describes the effect of increasing a sample size in a sampling distribution?
the distribution will get shorter.
the distribution will get wider.
the distribution will get narrower.
none of these.

Explanation:

Step1: Recall the formula for the standard deviation of the sampling distribution

The standard deviation of the sampling distribution of the sample mean \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step2: Analyze the effect of increasing \(n\)

As \(n\) (sample size) increases, the value of \(\frac{\sigma}{\sqrt{n}}\) decreases. A smaller standard deviation means that the data points in the sampling distribution are more concentrated around the mean. So the distribution gets narrower.

Answer:

The distribution will get narrower.