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When calculating a confidence interval for the population

Question: When calculating a confidence interval for the population mean with a known population standard deviation σ describe the effects of the following two changes on the confidence interval:

(1) doubling the sample size,

(2) quadrupling (multiplying by 4) the sample size.

Give two reasons why this relationship does not hold true if you are calculating a confidence interval for the population mean with an unknown population standard deviation.

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