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SE=(sigma)/(sqrtn)
The given equation relates the standard error, 
SE, of a sample mean to the population standard deviation, 
sigma, and the size of the sample, 
n. Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?
Choose 1 answer:
(A) 
n=((sigma)/(SE))^(2)
(B) 
n=(sigma^(2))/(SE)
(c) 
n=sqrt(((sigma)/(SE)))
(D) 
n=(sqrtsigma)/(SE)

SE=σn S E=\frac{\sigma}{\sqrt{n}} \newlineThe given equation relates the standard error, SE S E , of a sample mean to the population standard deviation, σ \sigma , and the size of the sample, n n . Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?\newlineChoose 11 answer:\newline(A) n=(σSE)2 n=\left(\frac{\sigma}{S E}\right)^{2} \newline(B) n=σ2SE n=\frac{\sigma^{2}}{S E} \newline(C) n=(σSE) n=\sqrt{\left(\frac{\sigma}{S E}\right)} \newline(D) n=σSE n=\frac{\sqrt{\sigma}}{S E}

Full solution

Q. SE=σn S E=\frac{\sigma}{\sqrt{n}} \newlineThe given equation relates the standard error, SE S E , of a sample mean to the population standard deviation, σ \sigma , and the size of the sample, n n . Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?\newlineChoose 11 answer:\newline(A) n=(σSE)2 n=\left(\frac{\sigma}{S E}\right)^{2} \newline(B) n=σ2SE n=\frac{\sigma^{2}}{S E} \newline(C) n=(σSE) n=\sqrt{\left(\frac{\sigma}{S E}\right)} \newline(D) n=σSE n=\frac{\sqrt{\sigma}}{S E}
  1. Given equation for standard error: We are given the equation for the standard error (SE) of a sample mean in terms of the population standard deviation (σ\sigma) and the size of the sample (nn):SE=σnSE = \frac{\sigma}{\sqrt{n}}We want to solve for nn in terms of SE and σ\sigma.
  2. Squaring both sides of the equation: First, we square both sides of the equation to eliminate the square root: \newline(SE)2=(σ2n)(SE)^2 = \left(\frac{\sigma^2}{n}\right)
  3. Isolating (σ)2(\sigma)^2 on one side: Next, we multiply both sides of the equation by nn to isolate (σ)2(\sigma)^2 on one side:\newlinen(SE)2=(σ)2n \cdot (SE)^2 = (\sigma)^2
  4. Solving for n: Then, we divide both sides of the equation by (SE)2(SE)^2 to solve for n:\newlinen=(σ)2(SE)2n = \frac{(\sigma)^2}{(SE)^2}
  5. Rewriting nn in terms of σ\sigma and SESE: We recognize that (σSE)2\left(\frac{\sigma}{SE}\right)^2 is the same as σ2SE2\frac{\sigma^2}{SE^2}, so we can rewrite nn as:\newlinen=(σSE)2n = \left(\frac{\sigma}{SE}\right)^2

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