Question 9 Doubling the size of the sample will reduce the standard error of the mean to one-half its current value. reduce the standard error of the mean to approximately $$ 70 \% $$ of its current value. have no effect on the standard error of the mean.

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Let the standard error of the mean (SEM) be expressed as

$$
\text{SEM} = \frac{\sigma}{\sqrt{n}},
$$

where $$\sigma$$ is the population standard deviation and $$n$$ is the sample size.

If the sample size is doubled, then the new sample size becomes $$2n$$. The new SEM is

$$
\text{SEM}_{\text{new}} = \frac{\sigma}{\sqrt{2n}} = \frac{\sigma}{\sqrt{2} \sqrt{n}} = \frac{1}{\sqrt{2}} \cdot \frac{\sigma}{\sqrt{n}}.
$$

Since

$$
\frac{1}{\sqrt{2}} \approx 0.707,
$$

the new standard error is approximately $$70\%$$ of the original standard error.

Thus, doubling the size of the sample reduces the standard error of the mean to roughly $$70\%$$ of its current value.
Doubling the sample size reduces the standard error of the mean to approximately 70% of its current value.

Question 9 Doubling the size of the sample will reduce the standard error of the mean to one-half its current value. reduce the standard error of the mean to approximately \( 70 \% \) of its current value. have no effect on the standard error of the mean.

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