In the 2004 election in Utah, 66% of all Utah voters voted for Amendment 3, the marriage amendment. Suppose a Statistics major decided to predict the sampling distribution of p̂ for samples of size 100 for this situation. What would happen to the standard deviation of the sampling distribution of p̂ if samples of size 500 were taken instead of samples of size 100?   The standard deviation would stay the same The standard deviation would increase The standard deviation would decrease

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In the 2004 election in Utah, 66% of all Utah voters voted for Amendment 3, the marriage amendment. Suppose a Statistics major decided to predict the sampling distribution of p̂ for samples of size 100 for this situation.

What would happen to the standard deviation of the sampling distribution of p̂ if samples of size 500 were taken instead of samples of size 100?
 

The standard deviation would stay the same
The standard deviation would increase
The standard deviation would decrease
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