Learning Outcomes
- Calculate the sample size needed for a given error bound for a confidence interval for a population proportion
Calculating the Sample Size n
If researchers desire a specific margin of error, then they can use the error bound formula to calculate the required sample size.
The error bound formula for a population proportion is
- EBP = [latex]\displaystyle({z}_{\frac{{\alpha}}{{2}}})(\sqrt{\frac{{p'q'}}{{n}}})[/latex]
- Solving for n gives you an equation for the sample size.
- [latex]\displaystyle{n}=\frac{{{\left({z}_{\frac{{\alpha}}{{2}}}\right)}^{2}({p'}{q'})}}{{{EBP}^{2}}}[/latex]
Example 5
Suppose a mobile phone company wants to determine the current percentage of customers aged 50+ who use text messaging on their cell phones. How many customers aged 50+ should the company survey in order to be 90% confident that the estimated (sample) proportion is within three percentage points of the true population proportion of customers aged 50+ who use text messaging on their cell phones?
try it 5
Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads on their smartphones?
