Lorraine was in a hurry when she computed a confidence interval for . Because was not known, she used a Student's t distribution. However, she accidentally used degrees of freedom n + 1 instead of n - 1. v Will her confidence interval be longer or shorter than one found using the correct degrees of freedom n - 1?

Answer

a.
shorter


b.
longer

The correct answer is option b: Longer.

To understand why using the incorrect degrees of freedom would result in a longer confidence interval, let's first understand what degrees of freedom represent in statistics. Degrees of freedom (df) is a concept that relates to the number of independent pieces of information that are available for estimating certain quantities in a statistical analysis.

In the case of computing a confidence interval, the correct degrees of freedom to use depend on the specific distribution being used. When computing a confidence interval for a population mean using Student's t distribution, the correct degrees of freedom to use is n - 1, where n is the sample size. The t-distribution accounts for the additional uncertainty introduced when estimating the population mean from a sample.

Using the incorrect degrees of freedom (n + 1 instead of n - 1) would imply that there is more information available than there actually is, which would result in a narrower distribution and narrower confidence interval. This means that Lorraine's confidence interval will be shorter compared to the correct confidence interval.

However, it is worth noting that using the incorrect degrees of freedom introduces bias into the calculation and can lead to inaccurate results. It is always important to use the correct degrees of freedom to obtain accurate and reliable confidence intervals.