SE=nσThe given equation relates the standard error, SE, of a sample mean to the population standard deviation, σ, 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=(SEσ)2(B) n=SEσ2(C) n=(SEσ)(D) n=SEσ
Q. SE=nσThe given equation relates the standard error, SE, of a sample mean to the population standard deviation, σ, 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=(SEσ)2(B) n=SEσ2(C) n=(SEσ)(D) n=SEσ
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) and the size of the sample (n):SE=nσWe want to solve for n in terms of SE and σ.
Squaring both sides of the equation: First, we square both sides of the equation to eliminate the square root: (SE)2=(nσ2)
Isolating (σ)2 on one side: Next, we multiply both sides of the equation by n to isolate (σ)2 on one side:n⋅(SE)2=(σ)2
Solving for n: Then, we divide both sides of the equation by (SE)2 to solve for n:n=(SE)2(σ)2
Rewriting n in terms of σ and SE: We recognize that (SEσ)2 is the same as SE2σ2, so we can rewrite n as:n=(SEσ)2