STAT 231 Lecture 1: q1.pdf
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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-
distribution substitute 2.05.
The ratio 1.96/2.05= .95609756
. di 1.96/2.05
.95609756
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