A random sample of size n is to be drawn from a population with a mean = 500 and sd = 100. What sample size would be necessary to ensure a standard error of 25? Sample sizes are whole numbers.

SEm = SD/√n

25 = 100/n

Solve for n.

To find the sample size necessary to ensure a standard error of 25, we need to use the formula for standard error:

Standard Error (SE) = population standard deviation / square root of sample size

In this case, the population standard deviation is given as 100, and we want the standard error to be 25. Plugging these values into the formula:

25 = 100 / √n

To solve for n, we can rearrange the equation:

√n = 100 / 25

Simplifying further:

√n = 4

To isolate n, we square both sides of the equation:

n = (4)^2

Therefore, the sample size necessary to ensure a standard error of 25 is:

n = 16

Hence, a sample size of 16 is required.