Question: Yi,..., Yn ~ N(u,o'). We've constructed a 1 - a confidence interval for a [) + to-1,0/25/vn]. and its length is proportional to 5, random.

Yi,..., Yn ~ N(u,o'). We've constructed a 1 - a confidence interval for a [) + to-1,0/25/vn]. and its length is proportional to 5, random. Show that P( the CI contains a|52 = #") is an increasing function of s'. Due to the randomness of S, we sometimes see long CIs and sometimes see short ones. One may think he/she is lucky if he/she sees a short one, seemingly more "accurate". However, it turns out that the conditional probabilities that the CI contains the true parameter a could also be small (in some cases, smaller than 1 - o)

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