Question

Compute the standard error for sample proportions from a population with proportion p= 0.55 for sample sizes of n=30, n=100 and n=1000 . Round your answers to three decimal places.

Answer 1

Given Information:

Population proportion = p =  0.55

Sample size 1 = n₁ = 30

Sample size 2 = n₂ = 100

Sample size 3 = n₃ = 1000

Required Information:

Standard error = σ = ?

Answer:

$\sigma_1 = 0.091$

$\sigma_2 = 0.050$

$\sigma_3 = 0.016$

Step-by-step explanation:

The standard error for sample proportions from a population is given by

$\sigma = \sqrt{\frac{p(1-p)}{n} }$  

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

For sample size n₁ = 30

$\sigma_1 = \sqrt{\frac{p(1-p)}{n_1} }$

$\sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} }$

$\sigma_1 = 0.091$

For sample size n₂ = 100

$\sigma_2 = \sqrt{\frac{p(1-p)}{n_2} }$

$\sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} }$

$\sigma_2 = 0.050$

For sample size n₃ = 1000

$\sigma_3 = \sqrt{\frac{p(1-p)}{n_3} }$

$\sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} }$

$\sigma_3 = 0.016$

As you can notice, the standard error decreases as the sample size increases.

Therefore, the greater the sample size lesser will be the standard error.