Question

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?

Answer 1

Step-by-step 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:

`M_S=\mu=65.`

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

`\sigma_S=(\sigma)/(√(n))=(15)/(√(9))=(15)/(3)=5.`

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:

`M_S=\mu=65.`

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

`\sigma_S=(\sigma)/(√(n))=(15)/(√(25))=(15)/(5)=3.`Answer

a.

• Expected mean value = ,65

,

• Expected standard error = ,5

b.

• Expected mean value = ,65

,

• Expected standard error = ,3