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Chapter 6: Problem 41

When we want \(95 \%\) confidence and use the conservative estimate of \(p=0.5,\) we can use the simple formula \(n=1 /(M E)^{2}\) to estimate the sample size needed for a given margin of error ME. In Exercises 6.40 to 6.43, use this formula to determine the sample size needed for the given margin of error. A margin of error of 0.02 .

Short Answer

Expert verified
The sample size required for a margin of error of 0.02 is 2500.

Step by step solution

01

Identify the given values

The conservative estimate \(p\) is given as 0.5 (however, it is not needed in calculation). The margin of error \(ME\) is provided as 0.02.
02

Substitute the values into the formula

Substitute the values into the formula \(n=1 /(M E)^{2}\). So \(n = 1 /(0.02)^2\).
03

Carry out the calculation

Carry out the calculation which gives \(n = 2500\).

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