STAT 231 Lecture 1: q1.pdf

Question 1: Relative width of confidence interval

The t-distribution converges to a Gaussian distribution. For infinite number of observations, the width

of the confidence interval for the t-distribution and the Gaussian distribution is the same. What is the

ratio of the width of a 95% confidence interval when using the Gaussian distribution divided by the

width of the T-distribution for n=30 observations.

Answer:

n=30 implies 29 d.f.

The width of the confidence interval is 2*1.96*se(mu) for the Gaussian distribution. For the t-