population has mean 53 and standard deviation 12. Calculate the standard deviation of x bar for a random sample of size 12.
I assume that you are talking about the standard error of the mean.
SEm = SD/√n
To calculate the standard deviation of the sample mean (x bar) for a random sample of size 12, you need to use the formula for the standard deviation of the sampling distribution of the mean.
The formula for the standard deviation of the sample mean is given by:
σ(x̄) = σ / √n
where:
- σ(x̄) is the standard deviation of the sample mean,
- σ is the standard deviation of the population,
- n is the sample size.
In this case, you are given that the population has a mean of 53 and a standard deviation of 12. The sample size is 12.
Substituting these values into the formula:
σ(x̄) = 12 / √12
To simplify this, you can take the square root of 12, which is approximately 3.464.
σ(x̄) = 12 / 3.464
Calculating this value gives:
σ(x̄) = 3.464
Therefore, the standard deviation of x bar for a random sample of size 12 is 3.464.