Researchers are estimating a population proportion using a sampling distribution of sample proportions with sample size \( n \). 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 \( \hat{p} \) decrease the sample proportion \( \hat{p} \)

To decrease the standard error of their sampling distribution, researchers should increase the sample size. The standard error of the sample proportion is calculated as \( \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \). By increasing \( n \), the denominator grows larger, which results in a smaller standard error, making their estimates more accurate and reliable. It's important to note that changing the sample proportion \( \hat{p} \) does not directly affect the standard error in the same way. In fact, the term \( \hat{p}(1 - \hat{p}) \) reaches its maximum when \( \hat{p} = 0.5 \), so the key focus should always be on increasing that sample size to tighten up your estimates!