When estimating the mean weight of stray cats using a single sample, which interval method is appropriate?

When estimating the mean weight of stray cats using a single sample, which interval method is appropriate?

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

Answer: (D)

Estimating a mean from one sample hinges on using the Student’s t distribution because the population standard deviation is unknown and is estimated from the sample. The one-sample t-interval uses the form mean ± t*(s/√n), where s is the sample standard deviation and t* comes from the t distribution with n−1 degrees of freedom. This accounts for extra uncertainty in estimating the spread, especially with smaller samples, making the interval wider than a z-interval would be if sigma were known. As the sample size grows, the t-interval behaves more like the z-interval, but the standard practice for a single sample with unknown sigma is to use the 1-sample t-interval. The z-interval would be appropriate only when the population standard deviation is known (or the sample is very large and the normal approximation is reliable), which isn’t the usual case for a single sample. The two-sample t-interval is used for comparing means from two different groups, not for estimating a single population mean. A nonparametric bootstrap interval is a valid alternative in some situations, but the standard approach taught for a single sample with unknown variance is the 1-sample t-interval.

Estimating a mean from one sample hinges on using the Student’s t distribution because the population standard deviation is unknown and is estimated from the sample. The one-sample t-interval uses the form mean ± t*(s/√n), where s is the sample standard deviation and t* comes from the t distribution with n−1 degrees of freedom. This accounts for extra uncertainty in estimating the spread, especially with smaller samples, making the interval wider than a z-interval would be if sigma were known. As the sample size grows, the t-interval behaves more like the z-interval, but the standard practice for a single sample with unknown sigma is to use the 1-sample t-interval.

The z-interval would be appropriate only when the population standard deviation is known (or the sample is very large and the normal approximation is reliable), which isn’t the usual case for a single sample. The two-sample t-interval is used for comparing means from two different groups, not for estimating a single population mean. A nonparametric bootstrap interval is a valid alternative in some situations, but the standard approach taught for a single sample with unknown variance is the 1-sample t-interval.