When no estimate of p is available, what planning value of p should be utilized for determining sample size?

In statistical sampling, when there is no prior estimate of the population proportion (p) available, the value that is commonly used for planning sample size calculations is 0.50. This is due to the fact that a proportion of 0.50 maximizes the required sample size, resulting in the most conservative estimation.

Using a value of 0.50 ensures that the sample size is sufficiently large to account for the highest variability in the population. When p is set at 0.50, the product of p and (1 - p) yields the largest result (0.25), which leads to the highest possible sample size needed to achieve a desired level of confidence and margin of error. This conservative approach is particularly important in ensuring that the sample will adequately represent the population, even when actual proportions may differ from 0.50.

In contrast, other values such as 0.25 or 0.75 would result in smaller sample sizes that may not adequately capture the variability in many situations, while a value of 1.00 does not apply as it indicates complete certainty rather than uncertainty, which is not typical in sampling scenarios. Therefore, using 0.50 as the planning value for p ensures robust and reliable sample size