Q.7.29 - Elementary Statistics

Question

Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

Step-by-Step Solution

Answer

The value of $\sigma \overline{x}$, depends on the sample size $n$. if we change $n$ the value of $\sigma \overline{x}$ i.e. standard deviation of all possible sample means differs.

Step 1: Given Information

We have to find The sample size have an effect on the standard deviation of all possible sample means.

Step 2: Explanation

$\sigma \overline{x}=\left\{\begin{array}{l}\sqrt{\frac{N-n}{N-1}·\frac{\sigma }{\sqrt{n}}}\\ \frac{\sigma }{\sqrt{n}}\end{array}\right.$if the sample is drawn without replacement.

if the sample is drawn with replacement:

Where 

$$\begin{gathered} n= Sample size \\ N =population size \end{gathered}$$

The value of $\sigma \overline{x}$, depends on the sample size $n$. if we change $n$the value of $\sigma \overline{x}$i.e. standard deviation of all possible sample means differs.