Question

Assume that the population proportion is 0.56. Compute the standard error of the proportion, σp, for sample sizes of 100, 200, 500, and 1,000. (Round your answers to four decimal places.)

Answer 1

Answer:

Standard errors are 0.049, 0.035, 0.022, and 0.016.

Step-by-step explanation:

The given value of population proportion (P) = 0.56

Given sample sizes (n ) 100, 200, 500, and 1000.

Now standard error is required to calculate.

Use the below formula to find standard error.

When sample size is n = 100

$\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{100}} =0.049$

When sample size is n = 200

$\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{200}} = 0.035$

When sample size is n = 500

$\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{500}} =0.022$

When sample size is n = 1000

$\sqrt{\frac{P(1-P)}{n}} = \sqrt{\frac{0.56(1-0.56)}{1000}} = 0.016$