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Find the sample size required to achieve the given margin of error with SD = 51.02 and z - score = 1.96. Round your answer to the nearest whole number. margin of error = 2

User Jason R
by
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1 Answer

6 votes

Answer:

The sample size required is 2500.

Explanation:

z-score:

In function of the margin of error M, the z-score is given by:


Z = (M)/((\sigma)/(√(n))) = (M√(n))/(\sigma)

In this question, we have that:


\sigma = 51.02, M = 2, Z = 1.96

So


Z = (M√(n))/(\sigma)


1.96 = (2√(n))/(51.02)


2√(n) = 51.02*1.96


√(n) = (51.02*1.96)/(2)


(√(n))^2 = ((51.02*1.96)/(2))^2


n = 2500

The sample size required is 2500.

User Avinash Joshi
by
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