A study with 18 observations aims to estimate the population mean with 95% confidence. Which method should be used for the confidence interval when the population standard deviation is unknown?

A study with 18 observations aims to estimate the population mean with 95% confidence. Which method should be used for the confidence interval when the population standard deviation is unknown?

• A. 1-sample t-interval with 17 degrees of freedom
• B. 1-sample z-interval
• C. 2-sample t-interval
• D. Chi-square interval

Answer: (A)

The key idea is that when you want a confidence interval for a population mean and the population standard deviation is unknown, you use the t-distribution. Replace the unknown sigma with the sample standard deviation and use the t critical value with degrees of freedom equal to n−1. Here, with 18 observations, that means a 1-sample t-interval with 17 degrees of freedom. The interval formula is x̄ ± t with 0.025 tail, 17 df, times (s/√n). The z-interval would be used only if sigma were known or the sample size were large enough for the normal to be a good approximation, and the other options relate to different problems (variance estimation or comparing two means).

The key idea is that when you want a confidence interval for a population mean and the population standard deviation is unknown, you use the t-distribution. Replace the unknown sigma with the sample standard deviation and use the t critical value with degrees of freedom equal to n−1. Here, with 18 observations, that means a 1-sample t-interval with 17 degrees of freedom. The interval formula is x̄ ± t with 0.025 tail, 17 df, times (s/√n). The z-interval would be used only if sigma were known or the sample size were large enough for the normal to be a good approximation, and the other options relate to different problems (variance estimation or comparing two means).