If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be:
A) 0.25.
B) 0.75.
C) either 0.20 or 0.80.
D) either 0.35 or 0.65.
E) either 0.30 or 0.70.

Question

Quizplus · Accepted Answer

The standard error of the sampling distribution of the sample proportion is given by the formula:

SE = sqrt[p(1-p) / n]

Where p is the population proportion and n is the sample size.

We are given SE = 0.0337 and n = 200. Substituting these values in the formula, we get:

0.0337 = sqrt[p(1-p) / 200]

Squaring both sides, we get:

0.00113569 = p(1-p) / 200

Multiplying both sides by 200, we get:

0.227138 = p(1-p)

This is a quadratic equation in p. Solving for p, we get:

p = 0.2 or p = 0.8

Therefore, the population proportion must be either 0.20 or 0.80. This is choice C.

If the Standard Error of the Sampling Distribution of the Sample