Question

Region

Populations (millions)
England
54.8
Wales
3.10
Scotland

4. The following table shows the population sizes of England, Wales, Scotland, and Northern Ireland.
A polling company wishes to ask questions of a stratified sample of the UK population, and decides that a sample size of 5000 people would be appropriate. Determine how many people from each region they should choose. (You can add a column to the right for your answers)

Answer 1

England = 4208 people

Wales = 238 people

Scotland = 412 people

Northern Ireland = 142 people

Explanation:

A polling company wishes to ask questions of a stratified sample of the UK population, and decides that a sample size of 5000 people would be appropriate.

To determine how many people from each region of the UK should be included in the stratified sample, we can use the proportion of each region's population relative to the total UK population.

First, calculate the total population:

`\begin{aligned}\textsf{Total UK Population} &=\sf 54.8+3.10+5.37+1.85\\&=\sf 65.12\; million\end{aligned}`

Now, determine the number of people to be chosen from each region by multiplying the proportion of each region (population of each region divided by the total population) by the sample size (5000):

`\boxed{\begin{aligned}\textsf{England} &=\sf (54.8)/(65.12) * 5000\\\\&=\sf 4207.6167076...\\\\&=\sf 4208\end{aligned}}`
`\boxed{\begin{aligned}\textsf{Wales} &=\sf (3.10)/(65.12) * 5000\\\\&=\sf 238.022113...\\\\&=\sf 238\end{aligned}}`

`\boxed{\begin{aligned}\textsf{Scotland} &=\sf (5.37)/(65.12) * 5000\\\\&=\sf 412.3157248...\\\\&=\sf 412\end{aligned}}`
`\boxed{\begin{aligned}\textsf{Northern Ireland} &=\sf (1.85)/(65.12) * 5000\\\\&=\sf 142.04545...\\\\&=\sf 142\end{aligned}}`

So, the number of people the polling company should choose from each region is:

• England = 4208 people
• Wales = 238 people
• Scotland = 412 people
• Northern Ireland = 142 people