A random sample of size n is to be drawn from a population with a mean = 1100 and SD = 300. What sample size would be necessary to ensure a standard error of 25? Sample sizes are whole numbers.
SEm = SD/√n
25 = 300/√n
Solve for n.
To calculate the necessary sample size, we can use the formula for the standard error:
Standard Error (SE) = Sample Standard Deviation (SD) / Square Root of Sample Size (n)
In this case, we are given that the population mean (μ) is 1100 and the population standard deviation (SD) is 300. We want the standard error (SE) to be 25.
Let's plug in the given values and the desired standard error into the formula:
25 = 300 / √n
To find the sample size (n), we need to isolate the variable. We can do this by rearranging the equation:
√n = 300 / 25
Simplifying the right side:
√n = 12
Now, square both sides to solve for n:
n = (12)^2
n = 144
So, a sample size of 144 would be necessary to ensure a standard error of 25.