Suppose a random sample of 80 measurements is selected from a population with a mean of 65 and a variance of 300. Select the pair that is the mean and standard error of x.
What are your choices?
Mean is most likely the same.
SEm = SD/√n
variance = SD^2
1.936
To find the mean and standard error of x, we need to use the formulas:
Mean of x: μx = μ (same as population mean)
Standard Error of x: σx = σ/√n
where:
μx = mean of x
μ = population mean
σx = standard error of x
σ = population standard deviation
n = sample size
Given information:
Population mean (μ) = 65
Population variance (σ^2) = 300
Sample size (n) = 80
So, to calculate the mean of x (μx), we can use the given population mean (μ):
μx = μ = 65
To calculate the standard error of x (σx), we can use the population standard deviation (σ) and sample size (n):
σx = σ/√n
First, we need to find the population standard deviation (σ) by taking the square root of the population variance (σ^2):
σ = √300 = 17.32 (rounded to two decimal places)
Next, we can calculate the standard error of x (σx):
σx = σ/√n = 17.32/√80 ≈ 1.938 (rounded to three decimal places)
Therefore, the pair that represents the mean and standard error of x is approximately:
Mean of x (μx) = 65
Standard Error of x (σx) ≈ 1.938