Question: In estimating a population mean with a confidence interval based on a random sample X1,... ,Xn from a Normal distribution with an unknown mean and

In estimating a population mean with a confidence interval based on a random sample X1,... ,Xn from a Normal distribution with an unknown mean and a known variance, how the length of the confidence interval changes if we decrease the sample size from 9n to n?

(a) The length of the confidence interval based on n samples is three times the length of the confidence interval based on 9n samples.

(b) The length of the confidence interval based on n samples is nine times the length of the confidence interval based on 9n samples.

(c) The length of the confidence interval based on n samples is one third of the length of the confidence interval based on 9n samples.

(d) The length of the confidence interval based on n samples is one ninth of the length of the confidence interval based on 9n samples.

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