For X∼Binomial(n=40,p=0.25)X \sim \text{Binomial}(n=40,p=0.25)X∼Binomial(n=40,p=0.25), the standard error of the sample proportion is
0.25×0.7540\sqrt{\frac{0.25 \times 0.75}{40}}400.25×0.75
400.25×0.75\sqrt{\frac{40}{0.25 \times 0.75}}0.25×0.7540
0.2540\frac{0.25}{\sqrt{40}}400.25
0.25×0.75\sqrt{0.25 \times 0.75}0.25×0.75