n=((1.96 sigma)/(E))^(2) Elon is planning a study of hours of internet use per month per household. He uses the given equation to determine the minimum number of randomly selected households, n, that he needs to include in his sample given a standard deviation of sigma hours and a maximum allowable error of E hours. Which of the following equations correctly gives the standard deviation in terms of the maximum allowable error and the minimum number of randomly selected households? Choose 1 answer: (A) sigma=sqrt((En)/(1.96)) (B) sigma=(Esqrtn)/(1.96) (C) sigma=sqrt((1.96 n)/(sigma))

Question

n=((1.96 sigma)/(E))^(2) Elon is planning a study of hours of internet use per month per household. He uses the given equation to determine the minimum number of randomly selected households,  n, that he needs to include in his sample given a standard deviation of  sigma hours and a maximum allowable error of  E hours. Which of the following equations correctly gives the standard deviation in terms of the maximum allowable error and the minimum number of randomly selected households? Choose 1 answer: (A)  sigma=sqrt((En)/(1.96)) (B)  sigma=(Esqrtn)/(1.96) (C)  sigma=sqrt((1.96 n)/(sigma))

Bytelearn · Accepted Answer

Given Equation: We start with the given equation: n = ((1.96 * sigma) / E)^2 We want to solve for sigma in terms of E and n.Square Root Elimination: First, we take the square root of both sides to eliminate the square on the right-hand side: sqrt(n) = sqrt(((1.96 * sigma) / E)^2)Simplify Right-hand Side: Simplifying the right-hand side, we get: sqrt(n) = (1.96 * sigma) / EIsolate Term with Sigma: Next, we multiply both sides by E to isolate the term with sigma: E * sqrt(n) = 1.96 * sigmaFinal Solution for Sigma: Finally, we divide both sides by 1.96 to solve for sigma: sigma = (E * sqrt(n)) / 1.96

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