Question

Calculate the percentage of the population sampled and

the finite population correction factor for each of the following

situations.

a. n= 1,000, N= 2,500

b. n= 1,000, N= 5,000

c. n= 1,000, N= 10,000

d. n= 1,000, N= 100,000

Short answer

a.The percentage of the population sample is 40% and the population correction factor is 0.774597

b.The percentage of the population sample is 20% and the population correction factor is 0.894427

c.The percentage of the population sample is 10% and the population correction factor is 0.948683

d. The percentage of the population sample is 1% and the population correction factor is 0.994987

Step-by-step solution

Given information

a. n= 1,000, N= 2,500

b. n= 1,000, N= 5,000

c. n= 1,000, N= 10,000

d. n= 1,000, N= 100,000

Finding the percentage of the population to sample and PCF

a.

The percentage of the population sample is

$\begin{array}{c}\text{Percentage\hspace{0.17em}of\hspace{0.17em}population\hspace{0.17em}sample}=\frac{n}{N}\times 100\%\\ =\frac{1000}{2500}\times 100\%\\ =40\%\end{array}$

The population correction factor is

$\begin{array}{c}\text{PCF}=\sqrt{1-\frac{n}{N}}\\ =\sqrt{1-\frac{1000}{2500}}\\ =\sqrt{0.60}\\ =0.7746\end{array}$

Finding the percentage of the population to sample and PCF

b.

The percentage of the population sample is

$\begin{array}{c}\text{Percentage\hspace{0.17em}of\hspace{0.17em}population\hspace{0.17em}sample}=\frac{n}{N}\times 100\%\\ =\frac{1000}{5000}\times 100\%\\ =20\%\end{array}$

The population correction factor is

$\begin{array}{c}\text{PCF}=\sqrt{1-\frac{n}{N}}\\ =\sqrt{1-\frac{1000}{5000}}\\ =\sqrt{0.80}\\ =0.8944\end{array}$

 Step 4: Finding the percentage of the population to sample and PCF

c.

The percentage of the population sample is

$\begin{array}{c}\text{Percentage\hspace{0.17em}of\hspace{0.17em}population\hspace{0.17em}sample}=\frac{n}{N}\times 100\%\\ =\frac{1000}{10000}\times 100\%\\ =10\%\end{array}$

The population correction factor is

$\begin{array}{c}\text{PCF}=\sqrt{1-\frac{n}{N}}\\ =\sqrt{1-\frac{1000}{10000}}\\ =\sqrt{0.90}\\ =0.9487\end{array}$

Finding the percentage of the population to sample and PCF

d.

The percentage of the population sample is

$\begin{array}{c}\text{Percentage\hspace{0.17em}of\hspace{0.17em}population\hspace{0.17em}sample}=\frac{n}{N}\times 100\%\\ =\frac{1000}{100000}\times 100\%\\ =1\%\end{array}$

The population correction factor is

$\begin{array}{c}\text{PCF}=\sqrt{1-\frac{n}{N}}\\ =\sqrt{1-\frac{1000}{100000}}\\ =\sqrt{0.99}\\ =0.9950\end{array}$