Answer:
a) The expected value of M = 40
The standard error for M = 4
b) The expected value of M = 40
The standard error for M = 2
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called the expected
value of M
- It is equal to the population mean μ
- The standard deviation of the distribution of sample means is called
the standard error of M
- The rule of standard error is σM = σ/√n , where σ is the standard
deviation and n is the size of the sample
* lets solve the problem
- A sample is selected from a population
∵ The mean of the population μ = 40
∵ The standard deviation σ = 8
a) The sample has n = 4 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 4
∴ σM = 8/√4 = 8/2 = 4
∴ The standard error for M = 4
b) The sample has n = 16 scores
∵ The expected value of M = μ
∵ μ = 40
∴ The expected value of M = 40
∵ The standard error of M = σ/√n
∵ σ = 8 and n = 16
∴ σM = 8/√16 = 8/4 = 2
∴ The standard error for M = 2
