When the hypothesized proportion is close to 0.50, the spread in the sampling distribution of is greater than when the hypothesized proportion is close to 0.0 or 1.0.

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The spread in the sampling distribution of a proportion is determined by the formula for the standard error of a proportion, which is sqrt[p(1-p)/n], where p is the hypothesized proportion and n is the sample size. When p is close to 0.50, the product p(1-p) reaches its maximum value, resulting in a greater spread in the sampling distribution compared to when p is close to 0.0 or 1.0, where the product p(1-p) is smaller.

When the Hypothesized Proportion Is Close to 0