APFIVE A researcher exploring brain activity in individuals with high math anxiety takes a random sample of 110 subjects. Expecting that 80% of the sampled individuals will experience brain activity similar to physical pain, the researcher needs the standard error for the sample proportion. Instead of correctly computing it as
$$SE=\sqrt{\frac{0.8\*0.2}{110}}\approx0.0381,$$
they mistakenly computed
$$SE=\sqrt{110\*0.8\*0.2}\approx4.195.$$
Identify and explain the mistake in this calculation.
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.
The researcher used an incorrect value for $$p$$; it should have been 0.75 instead of 0.80.
The mistake is in taking the square root; the standard error should be computed without applying the square root.
There is no mistake; both approaches yield equivalent results under the square root.
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