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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