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.
To find the mean and standard error of x, we first need to understand that x refers to the sample mean.
The mean of x, denoted as μx, will be equal to the population mean, which is 65.
The standard error of x, denoted as SE(x), is a measure of the variability or dispersion of the sample means from multiple random sampling. It represents the standard deviation of the distribution of sample means and is given by the formula:
SE(x) = σ / √n
where σ is the population standard deviation and n is the sample size.
In this case, you are given the population variance, which is the square of the standard deviation. So, we can calculate the population standard deviation (σ) as the square root of the population variance:
σ = √300
Next, we substitute the values into the formula for the standard error:
SE(x) = √300 / √80
Now, we simplify the expression:
SE(x) = 10 / √2
Therefore, the pair that represents the mean (μx) and standard error (SE(x)) of x is (65, 10/√2), where 10/√2 is the simplified form of the standard error.