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?
A)2.00
B)1.00
C)0.50
D)0.25

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?​
A)​2.00
B)​1.00
C)​0.50
D)​0.25

Quizplus · Accepted Answer

The z-score for a sample mean is calculated using the formula $z = \frac{M - \mu}{\sigma/\sqrt{n}}$, where $M$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{104 - 100}{32/\sqrt{16}} = \frac{4}{8} = 0.50$.

A Sample of N = 16 Scores Is Selected from a Population