Standard Error of a Sample Proportion

Question

A researcher takes a random sample of 110 subjects with high math anxiety. The population proportion expected to show a certain type of brain activity is 0.8. The researcher intends to calculate the standard error of the sample proportion. The correct calculation is $$SE=\sqrt{\frac{0.8(0.2)}{110}}\approx0.0381$$, but the researcher mistakenly computes $$SE=\sqrt{110(0.8)(0.2)}\approx4.195$$. Which of the following explains the error in the researcher's calculation?

Accepted Answer

The error is that the variance for a sample proportion should be calculated as $$\frac{p(1-p)}{n}$$, not $$n\*p(1-p)$$. The researcher did not divide by the sample size correctly.

Answer

The mistake is in taking the square root; the standard error should be computed without applying the square root.

Answer

There is no mistake; both approaches yield equivalent results under the square root.

Answer

The researcher used an incorrect value for $$p$$; it should have been 0.75 instead of 0.80.

Standard Error of a Sample Proportion

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