Respuesta :
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
When the sample has n = 4 scores then the expected value of M is 40 and the standard error of M is 4.
When the sample has n = 16 scores then the expected value of M is 40 and the standard error of M is 2.
Given
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?
The mean of the distribution of sample means is called the expected value of M.
The standard deviation of the distribution of sample means is called the standard error of M.
1. The sample has n = 4 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 4}\\\\ Standard \ error=\dfrac{8}{\sqrt{4}}\\\\ Standard \ error=\dfrac{8}{2}\\\\ Standard \ error=4[/tex]
The standard error for M = 4
2. 1. The sample has n = 16 scores
The expected value of M = μ
The expected value of M = 40
The standard error of M is;
[tex]\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 16}\\\\ Standard \ error=\dfrac{8}{\sqrt{16}}\\\\ Standard \ error=\dfrac{8}{4}\\\\ Standard \ error=2[/tex]
The standard error for M = 2
To know more about standard deviation click the link given below.
https://brainly.com/question/10984586
