A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?

Question

A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?

Answer 1

To calculate the z-score for a sample mean, we need to use the formula:

z = (M - μ) / (σ / √n)

Given the values in the question:
μ = 100 (population mean)
σ = 32 (population standard deviation)
M = 104 (sample mean)
n = 16 (sample size)

We can plug these values into the formula to calculate the z-score:

z = (104 - 100) / (32 / √16)
z = 4 / (32 / 4)
z = 4 / 8
z = 0.5

Therefore, the z-score for this sample mean is 0.5.

​A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?

To calculate the z-score for a sample mean, we need to use the formula:

A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?