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A sample is selected from a population with a mean ofu=65 and a standard deviation of o=15.a. If the sample has n=9 scores, what is the expectedvalue of M and the standard error of M?b. If the sample has n = 25 scores, what is theexpected value of M and the standard error of M?

A Sample Is Selected From A Population With A Mean Ofu65 And A Standard Deviation Of O15a If The Sample Has N9 Scores What Is The Expectedvalue Of M And The Sta class=

Sagot :

Explanation

From the statement, we have a sample selected from a population with:

• mean μ = 65,

,

• standard deviation σ = 15.

a. The sample has a size n = 9.

• From statistics, we know that the mean value of the sample Mₛ is equal to the mean of the population μ, so we have:

[tex]M_S=\mu=65.[/tex]

• The standard error of the sample σₛ is given by:

[tex]\sigma_S=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{9}}=\frac{15}{3}=5.[/tex]

b. The sample has a size n = 25.

• From statistics, we know that the mean value of the sample Mₛ is equal to the mean of the population μ, so we have:

[tex]M_S=\mu=65.[/tex]

• The standard error of the sample σₛ is given by:

[tex]\sigma_S=\frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{25}}=\frac{15}{5}=3.[/tex]Answer

a.

• Expected mean value = ,65

,

• Expected standard error = ,5

b.

• Expected mean value = ,65

,

• Expected standard error = ,3

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