A random sample of n = 9 scores is obtained from a population with ì = 50 and ó = 9. If the sample mean is M = 59, what is the z-score corresponding to the sample mean?
Z = (mean1 - mean2)/SEm
SEm = SD/√n
Insert values and calculate.
89
To calculate the z-score corresponding to the sample mean, we need to use the formula:
z = (M - μ) / (σ / √n)
where:
M = sample mean
μ = population mean
σ = population standard deviation
n = sample size
Let's plug in the given values:
M = 59
μ = 50
σ = 9
n = 9
Substituting these values into the formula:
z = (59 - 50) / (9 / √9)
= 9 / (9 / 3)
= 9 / 3
= 3
Therefore, the z-score corresponding to the sample mean is 3.