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Chapter 8: Q.8.1 (page 446)

Suppose we have data from a sample. The sample mean is 15, and the error bound for the mean is 3.2. What is the confidence interval estimate for the population mean?

Short Answer

Expert verified

The confidence interval estimate for the population mean is (11.8,18.2)

Step by step solution

01

Given Information 

Given in the question that,

sample mean =15

error bound for the mean =3.2

02

Step 2: 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 given by

x炉鈭�EBM鈮�渭鈮�x炉+EBM(1)

where EBM is the error bound for a population mean. We know that the sample mean is 15and the error bound for the mean is 3.2. Therefore x炉=15andEBM=3.2

So,from equation (1) we get

15鈭�3.2鈮�渭鈮�15+3.2

The confidence interval estimate for the population mean is (11.8,18.2). We say, "We estimate with 90% confidence that the true value of the population mean is between 11.8and 18.2," if the confidence level is 90% .x炉鈭�EBM鈮�渭鈮�x炉+EBM

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