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)It cannot be determined without knowing the population mean.

Question

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)​It cannot be determined without knowing the population mean.

Quizplus · Accepted Answer

To find the z-score of the sample mean, we need to calculate the standard error of the mean using the formula: 
SE = σ/√n
where σ is the population standard deviation and n is the sample size.
SE = 12/√16 = 3
The sample mean is 6 points greater than the population mean, so we can write: 
x̄ - μ = 6
where x̄ is the sample mean and μ is the population mean. Rearranging this equation, we have: 
x̄ = μ + 6
Substituting the values, we get: 
x̄ - μ = 6
(μ + 6) - μ = 6
6 = 6
This means that the sample mean is exactly 6 points greater than the population mean. Therefore, the z-score for the sample mean is: 
z = (x̄ - μ)/SE = 6/3 = 2
So, the answer is B (z-score of 2).

A Random Sample of N = 16 Scores Is Obtained