Suppose you have decided to gather some fixed number n of observations, and crea

Question

Suppose you have decided to gather some fixed number n of observations, and create a confidence interval at some confidence level c, where the variance of the underlying population is known to be o^2. Before you even gather your n numbers, you already know how long the confidence interval will be. Explain why. Suppose you have decided to gather some fixed number n of observations, and create a confidence interval at some confidence level c, where the variance of the underlying population is known to be o^2. Before you even gather your n numbers, you already know how long the confidence interval will be. Explain why.

Explanation / Answer

because the confidence interval is mainly characterized by the confidence level c.

it is the c that defines the length of the confidence interval.

in general if [T1,T2] be the confidence interval then its length l=T2-T1 is independent of n and solely depends on c.

hence even before gathering n numbers, you already know how long the confidence interval will be

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