A weight study of 24 newly admitted stray cats aims to estimate their mean weight. Which method provides a confidence interval for the mean weight?

A weight study of 24 newly admitted stray cats aims to estimate their mean weight. Which method provides a confidence interval for the mean weight?

• A. 2-sample t-interval
• B. Z-interval
• C. 1-sample t-interval
• D. Paired t-interval

Answer: (C)

When estimating a single population mean from one sample, and the population standard deviation is unknown, use the 1-sample t-interval. Here you have a single group of 24 stray cats and you want a confidence interval for their mean weight, so you estimate the mean with x-bar and use the t distribution with 23 degrees of freedom (n−1). This yields x-bar ± t_(0.025, 23) × s/√n. The Z-interval would require knowing the true population SD, which is rarely available. The other options are for different designs—comparing two means or analyzing paired measurements—so they’re not appropriate here.

When estimating a single population mean from one sample, and the population standard deviation is unknown, use the 1-sample t-interval. Here you have a single group of 24 stray cats and you want a confidence interval for their mean weight, so you estimate the mean with x-bar and use the t distribution with 23 degrees of freedom (n−1). This yields x-bar ± t_(0.025, 23) × s/√n. The Z-interval would require knowing the true population SD, which is rarely available. The other options are for different designs—comparing two means or analyzing paired measurements—so they’re not appropriate here.