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
