Respuesta :
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:
[tex]$ \sigma_1 = 0.091 $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
Step-by-step explanation:
The standard error for sample proportions from a population is given by
[tex]$ \sigma = \sqrt{\frac{p(1-p)}{n} } $[/tex]
Where p is the population proportion and n is the sample size.
For sample size n₁ = 30
[tex]$ \sigma_1 = \sqrt{\frac{p(1-p)}{n_1} } $[/tex]
[tex]$ \sigma_1 = \sqrt{\frac{0.55(1-0.55)}{30} } $[/tex]
[tex]$ \sigma_1 = 0.091 $[/tex]
For sample size n₂ = 100
[tex]$ \sigma_2 = \sqrt{\frac{p(1-p)}{n_2} } $[/tex]
[tex]$ \sigma_2 = \sqrt{\frac{0.55(1-0.55)}{100} } $[/tex]
[tex]$ \sigma_2 = 0.050 $[/tex]
For sample size n₃ = 1000
[tex]$ \sigma_3 = \sqrt{\frac{p(1-p)}{n_3} } $[/tex]
[tex]$ \sigma_3 = \sqrt{\frac{0.55(1-0.55)}{1000} } $[/tex]
[tex]$ \sigma_3 = 0.016 $[/tex]
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.
