Question

Assume that the population proportion is 0.46. Compute the standard error of the proportion, om, for sample sizes of 500,000; 1,000,000; 5,000,000; 10,000,000; and 100,000,000. (Round your answers to five decimal places.) sample size of 500,000 sample size of 1,000,000 sample size of 5,000,000 sample size of 10,000,000 sample size of 100,000,000 What can you say about the size of the standard error of the sample proportion as the sample size is increased? The standard error of the sample proportion, on ---Select--- and becomes extremely ---Select--- as the sample size becomes huge.

Answer 1

Solution

given: p=0.46, (1-P) = 0.54

p(1-P) formula : Standard error (op) = n

for n 500,000, Standard error (op) = 0.46 * 0.54 V 500000 = 0.00070

0.54 for n= 1,000,000, Standard error (op) = 0.46 * V 1000000 = 0.00050

for n= 5,000,000, Standard error (op) = 0.46 * 0.54 V 5000000 = 0.00022

for n 10,000,000, Standard error (op) = 0.46 * 0.54 V 10000000 0.00016

* 0.54 for n 100,000,000, Standard error (op) 0.46 V 100000000 = 0.00005

The standard error of the sample proportion,_{$\small \sigma_{\hat p}$},
decreases
and becomes extremely
small
as the sample size becomes huge.