To compute the error between the sample mean and the population mean, we calculate the standard error of the mean (SEM). The formula for the standard error is:

$\text{Standard Error (SEM)} = \frac{\sigma}{\sqrt{n}}$

Where:

• $\sigma$ is the population standard deviation,
• $n$ is the sample size.

a) For $n = 4$:

$\text{SEM} = \frac{20}{\sqrt{4}} = \frac{20}{2} = 10$

So, the expected error is 10.

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b) For $n = 16$:

$\text{SEM} = \frac{20}{\sqrt{16}} = \frac{20}{4} = 5$

So, the expected error is 5.

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c) For $n = 100$:

$\text{SEM} = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2$

So, the expected error is 2.

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Final Answers:

• (a) 10
• (b) 5
• (c) 2

Would you like a further explanation of this concept or assistance with similar questions?

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Here are 5 follow-up questions to expand your understanding:

1. How does increasing the sample size affect the standard error of the mean?
2. Why is the standard error smaller for larger sample sizes?
3. Can the standard error ever equal the population standard deviation?
4. How does the standard error relate to the Central Limit Theorem?
5. What happens to the standard error if the population standard deviation increases?

Tip: The standard error decreases with larger sample sizes because averaging over more data points reduces variability.