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Chapter 6: Problem 43

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 0.05 .

Short Answer

Expert verified
The required sample size to achieve a margin of error of 0.05 with the conservative estimate of \(p=0.5\) and \(95\%\) confidence is \(400\).

Step by step solution

01

Understand the Given Values

The task mentions a target confidence level of \(95 \% \) and a conservative estimate for proportion \(p=0.5\). We are given a formula to estimate the sample size needed for a given margin of error \(ME\), i.e., \(n=1 /(M E)^{2}\). The given margin of error is \(0.05\).
02

Substitute values into formula

Substitute \(ME = 0.05\) into the formula \(n=1 /(M E)^{2}\). This gives \(n = 1 /(0.05)^{2}\).
03

Solve for n

Calculate the value for \(n\). Using the formula from step 2 gives \(n = 1 /(0.05)^{2} = 400\). Thus, a sample size of 400 is needed to achieve a margin of error of 0.05.

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Most popular questions from this chapter

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