The standard error of p̅ can be calculated using which formula?

The standard error of the sample proportion, denoted as p̅, is an important concept in statistics that measures the variability of the sample proportion from the true population proportion p. The formula for the standard error of p̅ is derived from the concept of sampling distributions.

The correct formula, SQRT((p(1-p)) / (n)), accurately represents how the variability of the sample proportion is affected by the population proportion (p) and the sample size (n). Specifically, in this formula:

• p is the true population proportion of successes.
• (1 - p) is the proportion of failures.
• n is the sample size.
• The square root is used because the standard error is based on the variance of the sampling distribution, which takes the square root of the calculations for variability.

This formula illustrates that as the sample size (n) increases, the standard error decreases, leading to a more precise estimate of the population proportion. Essentially, a larger sample provides a better approximation of the true proportion.

In contrast, the other formulas provided do not represent the standard error of the sample proportion. They either relate to different statistical concepts or lack the components necessary to calculate the standard error accurately. Thus, the first option distinctly reflects the