The situations that would result in the smallest standard deviation of p is; The population proportion p ≠ 0.5, and the sample size is n.
What is the standard deviation?
The formula for the standard deviation here is;
SD = √(n(p(1 - p))
Now, for the standard deviation to be maximum, it means that p = 0.5 and as such 1 - p will also be 0.5.
However, for Standard deviation to be smallest, then it means that p ≠ 0.5.
Secondly, for the sample size, it will have to remain as n and not 2n because when we say 2n, we are increasing the sample size which will in turn increase the standard deviation.
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