Researchers are estimating a population proportion using a sampling distribution of sample proportions with sample size . I
the researchers want to decrease the standard error of their sampling distribution they should…
increase the sample size
decrease the sample size
increase the sample proportion
decrease the sample proportion

Ask by Nguyen Johnson. in the United States

Mar 14,2025

Question

Researchers are estimating a population proportion using a sampling distribution of sample proportions with sample size . I
the researchers want to decrease the standard error of their sampling distribution they should…
increase the sample size
decrease the sample size
increase the sample proportion
decrease the sample proportion

Ask by Nguyen Johnson. in the United States

Mar 14,2025

UpStudy AI · Accepted Answer

Consider the formula for the standard error of the sample proportion:

$$
\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}
$$

where:
- $$ p $$ is the true population proportion.
- $$ n $$ is the sample size.

Notice that the standard error $$ \sigma_{\hat{p}} $$ is inversely related to the square root of the sample size $$ n $$. This means that as the sample size increases, the standard error decreases.

Therefore, to decrease the standard error of the sampling distribution, the researchers should:

- **increase the sample size**.
To decrease the standard error of the sampling distribution, the researchers should **increase the sample size**.

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