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Chapter 8: Q.8.6 (page 455)

Suppose we know that a confidence interval is (42.12,47.88). Find the error bound and the sample mean.

Short Answer

Expert verified

The error bound and the sample mean are:

x炉=45EMB=2.88.

Step by step solution

01

Given Information

The term "error bound,'' is an upper bound on the size of the error

02

Explanation

If x-is the sample mean of a random sample of size n from a normal population with known variance, a Cl (confidence interval) on 渭is provided by

x炉鈭�EBM鈮�渭鈮�x炉+EBM

Where EBM is the error bound for a population mean.

We know that Cl is (42.12,47.88), but we do not know the sample mean and the error bound for the mean. Therefore sample mean is

x炉=42.12+47.882=45

and error bound is

EBM=47.88鈭�42.122=2.88

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