Researchers are estimating a population proportion using a sampling distribution of sample proportions with sample size \( n \). If 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 \( \hat{p} \)
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To decrease the standard error of the sampling distribution, researchers should increase the sample size. The standard error is inversely related to the square root of the sample size (\( n \)); as \( n \) increases, the standard error decreases. This allows for more precise estimation of the population proportion. Moreover, sample proportions \( \hat{p} \) do not directly affect the standard error in terms of decreasing it; instead, it's a function of variability within the sample. Maintaining a larger sample size mitigates variability and leads to more reliable estimates of the population proportion.