Question

A sample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores, what is the expected value of M and the standard error of M? b. If the sample has n = 16 scores, what is the expected value of M and the standard error of M? Gravetter, Frederick J. Statistics for The Behavioral Sciences (p. 221). Cengage Learning. Kindle Edition.

Answer 1

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