Sample Statistics

Definition

Sample statistics are numerical measures calculated from a sample of data that provide information about the characteristics of the population from which the sample was drawn. They are used to estimate and make inferences about the unknown parameters of the population.

5 Must Know Facts For Your Next Test

1. Sample statistics are used to estimate unknown population parameters, such as the population mean, population proportion, or population variance.
2. The Central Limit Theorem is a key concept in understanding the properties of sample statistics and their relationship to population parameters.
3. As the sample size increases, the sampling distribution of the sample mean becomes more normal in shape, even if the population distribution is non-normal.
4. The standard error of the sample mean, which is the standard deviation of the sampling distribution of the sample mean, decreases as the sample size increases.
5. Sample statistics, such as the sample mean and sample proportion, are unbiased estimators of the corresponding population parameters.

Review Questions

• Explain how the Central Limit Theorem relates to the properties of sample statistics.
  • The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. This has important implications for the properties of sample statistics, such as the sample mean and sample proportion. As the sample size increases, the sampling distribution of the sample mean becomes more normal in shape, and the standard error of the sample mean decreases. This allows us to make more accurate inferences about the population parameters using the sample statistics.
• Describe how sample statistics are used to estimate unknown population parameters.
  • Sample statistics, such as the sample mean and sample proportion, are used to estimate the corresponding unknown population parameters, such as the population mean and population proportion. These sample statistics are unbiased estimators, meaning that their expected value is equal to the true population parameter. By taking a representative sample from the population and calculating the sample statistics, we can make inferences about the population characteristics and use the sample statistics to estimate the unknown population parameters.
• Analyze how the sample size affects the properties of sample statistics and the accuracy of population inferences.
  • As the sample size increases, the properties of the sample statistics, such as the sample mean and sample proportion, become more desirable for making inferences about the population. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This means that the standard error of the sample mean, which is the standard deviation of the sampling distribution, decreases as the sample size increases. Consequently, larger sample sizes allow for more accurate estimation of population parameters and more reliable statistical inferences about the population.

Related terms

Population Parameter: A numerical measure that describes a characteristic of an entire population, such as the population mean or population proportion.

Sample: A subset of a population that is selected to represent the entire population for the purpose of making inferences.

Central Limit Theorem: A fundamental result in probability and statistics that states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.