Answer
The standard deviation of p̂ decreases with an increase in sample size. If the sample size is increased by a factor of 4, the standard deviation of p̂ will decrease by a factor of 2 (because of the square root in the equation).
Work Step by Step
The standard deviation of p̂ decreases with an increase in sample size. If the sample size (n) is increased by a factor of 4, the standard deviation of p̂ will decrease by a factor of 2 because of the square root in the equation, i.e. $\sigma=\sqrt{\frac{p(1-p)}{n}}$.
