Standard Deviation for Sample Proportions

Question

All of the following statements about the standard deviation of the sampling distribution for sample proportions are true EXCEPT:
 
Standard Deviation for Sample Proportions:

| Parameter                  | Expression                      |
|----------------------------|---------------------------------|
| Standard Error of $$\hat{p}$$ | $$\sqrt{\frac{p(1-p)}{n}}$$      |
| Dependence on n            | Inversely proportional to $$\sqrt{n}$$ |

Accepted Answer

The standard deviation of the sampling distribution for sample proportions is independent of the sample size.

Answer

The standard deviation for the sample proportion is given by $$\sqrt{\frac{p(1-p)}{n}}$$, assuming a sufficiently large sample.

Answer

Increasing the sample size decreases the standard error of the sample proportion.

Answer

For the normal approximation to hold, both $$np$$ and $$n(1-p)$$ should be at least 10.

Parameter	Expression
Standard Error of $$\hat{p}$$	$$\sqrt{\frac{p(1-p)}{n}}$$
Dependence on n	Inversely proportional to $$\sqrt{n}$$

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