A random sample of n = 16 scores is obtained from a population with σ = 12.If the sample mean is 6 points greater than the population mean,what is the z-score for the sample mean?
A)+6.00
B)+2.00
C)+1.00
D)Cannot be determined without knowing the population mean

Question

Quizplus · Accepted Answer

We can use the formula 
z = (x̄ - μ) / (σ/√n)
where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Since we know that the sample mean is 6 points greater than the population mean, we can write:
x̄ = μ + 6

Substituting this into the formula, we get:
z = (μ + 6 - μ) / (12/√16)
z = 2

Therefore, the z-score for the sample mean is +2.00.

A Random Sample of N = 16 Scores Is Obtained