Samples of n = 16 scores are selected from a population.If the distribution of sample means has an expected value of 40 and a standard error of 2,what is the mean and the standard deviation for the population?
A)µ = 40 and σ = 2
B)µ = 40 and σ = 8
C)µ = 40 and σ = 32
D)µ = 160 and σ = 2

Question

Quizplus · Accepted Answer

The mean of the distribution of sample means is equal to the mean of the population, which is given as 40. 
The standard deviation of the distribution of sample means (standard error) is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, 
2 = σ / sqrt(16) 
2 = σ / 4 
σ = 8 
Therefore, the correct answer is B, with a mean of 40 and a standard deviation of 8 for the population.

Samples of N = 16 Scores Are Selected from a Population.If