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Chapter 8: Q 8.43 (page 330)

Discuss the relationship between the margin of error and the standard error of the mean.

Short Answer

Expert verified

The margin of error and the standard error of the mean are directly proportional to each other.

Step by step solution

01

Given Information

Margin of error is represented by E.

Standard error of sample mean is represented byσn.

02

Explanation

Mathematically, the relationship between the two is represented by

E=zα/2×σn

The above relation is true for 100(1-α)%Clof population mean μ.

Hence, margin of error is product of za/2and standard error of sample mean.

Therefore, margin of error is directly proportional to standard error of the mean.

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