Question

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

Answer 1

Shorter. As the degrees of freedom increase, the value for tc decreases.

Answer 2

The confidence interval will be shorter

Explanation:

Required

How will the confidence interval be affected when n is used instead of n - 1

As sample size n increases, the confidence interval also increases by 1;

i.e.

`df = n- 1`

However, the confidence interval gets reduced.

This implies that, the higher the degrees of freedom; the shorter the confidence interval.