Mathematics, 25.06.2019 01:00 madams1820

Asample 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.

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Answer from: xlxJazmin

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;

$\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 4}\\\\ Standard \ error=\dfrac{8}{\sqrt{4}}\\\\ Standard \ error=\dfrac{8}{2}\\\\ Standard \ error=4$

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;

$\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\ \sigma = 8 \ and \ n = 16}\\\\ Standard \ error=\dfrac{8}{\sqrt{16}}\\\\ Standard \ error=\dfrac{8}{4}\\\\ Standard \ error=2$

The standard error for M = 2

To know more about standard deviation click the link given below.

link

Answer from: ab847150

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

Answer from: Quest

Dis a correct answer

Answer from: Quest

this doesn't make sense lol

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Asample is selected from a population with a mean of μ = 40 and a standard deviation of σ = 8. a. if...