SAT scores are normally distributed with a mean of 500 and a standard deviation of 100. Using the formula for σM, what will σM be when
a. the sample size is 25
b. the sample size is 121, and
c. the sample size is 400?
To find σM (the standard error of the mean), we can use the formula:
σM = σ / sqrt(n)
Where σ is the population standard deviation and n is the sample size.
Given that the population standard deviation is σ = 100,
a. For a sample size of 25, σM = σ / sqrt(n) = 100 / sqrt(25) = 100 / 5 = 20.
b. For a sample size of 121, σM = σ / sqrt(n) = 100 / sqrt(121) = 100 / 11 = 9.09 (rounded to two decimal places).
c. For a sample size of 400, σM = σ / sqrt(n) = 100 / sqrt(400) = 100 / 20 = 5.
So, σM will be 20, 9.09, and 5 for sample sizes of 25, 121, and 400, respectively.