3.5 Sample Size for Population Proportion Studies



Often researchers want to know the smallest sample size they need in order to create a confidence interval with a specific margin of error. The margin of error is dependent on the sample size.

  1. Suppose an internet marketing company wants to determine the current percentage of customers who click on ads. How many customers should the company survey to be 90% confident that the estimated proportion is within five percentage points of the true population proportion of customers who click on ads?
    1. What is the confidence level for the study? 0.90
    2. What is the margin of error the company will tolerate in their study? 0.05
    3. What is the sample size required for the study? 271


    2. Steps in StatCrunch

    • Click on Stats → Proportion Stats → One Sample → Width/Sample Size
    • Enter the confidence level as a real number in decimal form
    • If no previous estimate is given, leave 0.5 as the target proportion. If a previous estimate of \(\hat{p}\) is given from a previous study, enter it as the target proportion.
    • Enter the width of the confidence interval. Remember, the width is TWICE the margin of error. The margin of error is usually stated as “within k%.” Change the margin of error into a real number decimal and multiply by 2.
    • Click Compute
    • StatCrunch will give the sample size, rounded to the appropriate whole number value.

  2. You wish to estimate, with 99% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. You want your estimate to be accurate to within 4% of the true population proportion. A prior study found that 31% of motor vehicle fatalities were caused by alcohol-impaired driving. Find the minimum sample size needed.
    1. What is the confidence level for the study? 0.99
    2. What is the margin of error for the study? 0.04
    3. What is the target proportion for the study? 0.31
    4. How many motor vehicle fatalities should you include in your study? 888

  3. Suppose a mobile phone company want to determine the current percentage of customers over 65-years-old who use text messaging on their cell phones. How many customers over 65-years-old should the company survey in order to be 95% confident that the estimated proportion is within three percentage points of the true population proportion of customers over 65 who text on their phones? 1068