In which of the following situations is it appropriate to use the confidence interval formula for a proportion ($p$)?

• A. When calculating the average income of a group of people
• B. When determining the standard deviation ($\sigma$) of test scores in a class
• C. When estimating the percentage of voters who support a particular candidate based on a random sample ($p$)
• D. When estimating the mean ($\mu$) height of a population using sample data

Answer: (C)

Verified step by step guidance

1. Understand that the confidence interval formula for a proportion is used when estimating the true proportion (or percentage) of a population that has a certain characteristic, based on sample data.
2. Recognize that this method applies when the data is categorical (e.g., yes/no, support/do not support) rather than numerical measurements like income, height, or test scores.
3. Identify that calculating the average income or mean height involves numerical data and requires confidence intervals for means, not proportions.
4. Note that determining the standard deviation of test scores is about measuring variability, not estimating a proportion, so the proportion confidence interval is not appropriate.
5. Conclude that the correct situation to use the confidence interval formula for a proportion is when estimating the percentage of voters who support a particular candidate based on a random sample, since this involves estimating a population proportion from categorical data.