A factory foreman estimates mean daily shirts produced as 230 with standard deviation 13; he constructs a 95% confidence interval for the mean using a t-interval. Which method is used?

A factory foreman estimates mean daily shirts produced as 230 with standard deviation 13; he constructs a 95% confidence interval for the mean using a t-interval. Which method is used?

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

Answer: (C)

Estimating a population mean from one sample when the population standard deviation is unknown calls for a t-interval. Here you have a single sample with a reported mean and a sample standard deviation, and you’re constructing a confidence interval for the mean. Since sigma is unknown and you’re drawing inferences from one sample, the appropriate distribution is the t distribution, not z, and you use the one-sample t-interval formula. The interval relies on the t-critical value with degrees of freedom equal to the sample size minus one. That’s why the method used is a one-sample t-interval. The other options don’t fit: a z-interval would be used only if the population standard deviation were known or the sample were large enough for a robust z approximation; a two-sample t-interval compares means from two independent samples; a paired t-interval is for dependent measurements on the same subjects.

Estimating a population mean from one sample when the population standard deviation is unknown calls for a t-interval. Here you have a single sample with a reported mean and a sample standard deviation, and you’re constructing a confidence interval for the mean. Since sigma is unknown and you’re drawing inferences from one sample, the appropriate distribution is the t distribution, not z, and you use the one-sample t-interval formula. The interval relies on the t-critical value with degrees of freedom equal to the sample size minus one.

That’s why the method used is a one-sample t-interval. The other options don’t fit: a z-interval would be used only if the population standard deviation were known or the sample were large enough for a robust z approximation; a two-sample t-interval compares means from two independent samples; a paired t-interval is for dependent measurements on the same subjects.