Which interval estimate would be used to estimate the population proportion of successes from a sample?

Which interval estimate would be used to estimate the population proportion of successes from a sample?

• A. 1-sample t-interval
• B. 2-proportion z-interval
• C. 1-proportion z-interval
• D. 2-sample t-interval

Answer: (C)

Estimating a population proportion from a sample is done with a one-proportion z-interval. You use the sample proportion p̂ as the best guess for the true proportion p, and you form the interval with p̂ ± z* sqrt[p̂(1−p̂)/n], where z* is the z-score for your confidence level. This works because the distribution of p̂ is approximately normal when the sample is large enough (np̂ and n(1−p̂) are reasonably big), which justifies the standard normal-based margin of error. T-intervals are for estimating a mean when the population standard deviation is unknown, not for proportions. Intervals based on two samples are for comparing two proportions or two means, not for estimating a single population proportion. So the appropriate interval is the one-proportion z-interval.

Estimating a population proportion from a sample is done with a one-proportion z-interval. You use the sample proportion p̂ as the best guess for the true proportion p, and you form the interval with p̂ ± z* sqrt[p̂(1−p̂)/n], where z* is the z-score for your confidence level. This works because the distribution of p̂ is approximately normal when the sample is large enough (np̂ and n(1−p̂) are reasonably big), which justifies the standard normal-based margin of error. T-intervals are for estimating a mean when the population standard deviation is unknown, not for proportions. Intervals based on two samples are for comparing two proportions or two means, not for estimating a single population proportion. So the appropriate interval is the one-proportion z-interval.