Question

Question 4 0.66/2 View Policies Show Attempt History Current Attempt in Progress - Your answer is partially correct. Impact of Sample Size on Accuracy Compute the standard error for sample proportions from a population with proportion p=0.75 for sample sizes of n = 30 n = 200 , and n = 1100 Round your answers to three decimal places. Standard Error Sample Size n = 30 0.086 n = 200 0.031 n = 1100 0.0080

Answer 1

Solution:

Given: p = 0.75

Sample sizes : n = 30,n = 200 , n = 1100

We have to find standard error for these sample sizes.

Formula:

px (1-p)

Standard error for n = 30 is:

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times (1-0.75)}{30 }}$

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times 0.25 }{30 }}$

$\sigma_{\hat{p}}= \sqrt{ 0 .00625 }$

$\sigma_{\hat{p}}= 0.079$

Standard error for n = 200 is:

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times (1-0.75)}{20 0 }}$

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times 0.25 }{20 0 }}$

$\sigma_{\hat{p}}= \sqrt{ 0.0009375 }$

$\sigma_{\hat{p}}= 0.031$

Standard error for n = 1100 is:

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times (1-0.75)}{11 0 0 }}$

$\sigma_{\hat{p}}= \sqrt{\frac{0.75 \times 0.25 }{1100 }}$

$\sigma_{\hat{p}}= \sqrt{ 0.000170455 }$

$\sigma_{\hat{p}}= 0.013$