Math Problem Statement

Do the sample means target the population mean? In general, do sample means make good estimates of population means? Why or why not?

Solution

The question in the image asks about how sample means relate to the population mean and whether sample means are good estimates of population means.

Here’s how the blanks should be filled:

  1. The sample means target the population mean. This means that the sample mean tends to approach the population mean as the sample size increases.

  2. In general, sample means do make good estimates of population means because the mean is an unbiased estimator.

So the filled-in statement would be:

  • "The sample means target the population mean. In general, sample means do make good estimates of population means because the mean is an unbiased estimator."

Would you like further details or explanations on this?

Here are 5 relative questions:

  1. Why is the sample mean considered an unbiased estimator?
  2. How does the sample size affect the accuracy of the sample mean?
  3. What is the difference between biased and unbiased estimators?
  4. In what scenarios might a sample mean not be a good estimate of the population mean?
  5. How does the central limit theorem relate to sample means?

Tip: Increasing the sample size tends to make the sample mean a more accurate estimator of the population mean because variability decreases as more data is included.

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Math Problem Analysis

Mathematical Concepts

Statistics
Estimators
Central Limit Theorem

Formulas

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Theorems

Law of Large Numbers
Unbiased Estimator Property

Suitable Grade Level

College