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We want to estimate mean of a distribution by taking i.i.d. measurements, and computing their sample mean. Suppose we might be able to improve the precision of the measurements by refining the experiments, meaning we might be able to reduce the variance of the measurements (up to a point). Assuming we want to estimate the mean by conducting exactly 100 experiments, with an error of at most 1 unit and 99% certainty, how low should the variance be (approximately)?

We want to estimate mean of a distribution by taking i.i.d. measurements, and computing their sample mean. Suppose we might be able to improve the precision of the measurements by refining the experiments, meaning we might be able to reduce the variance of the measurements (up to a point). Assuming we want to estimate the mean by conducting exactly 100 experiments, with an error of at most 1 unit and 99% certainty, how low should the variance be (approximately)?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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We want to estimate mean of a distribution by taking i.i.d. measurements, and computing their sample mean. Suppose we might be able to improve the precision of the measurements by refining the experiments, meaning we might be able to reduce the variance of the measurements (up to a point). Assuming we want to estimate the mean by conducting exactly 100 experiments, with an error of at most 1 unit and 99% certainty, how low should the variance be (approximately)?
Transcribed Image Text:We want to estimate mean of a distribution by taking i.i.d. measurements, and computing their sample mean. Suppose we might be able to improve the precision of the measurements by refining the experiments, meaning we might be able to reduce the variance of the measurements (up to a point). Assuming we want to estimate the mean by conducting exactly 100 experiments, with an error of at most 1 unit and 99% certainty, how low should the variance be (approximately)?
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