Population Parameter

Definition

A population parameter is a numerical characteristic or measurement that describes the entire population being studied. It is a fixed, unknown value that represents the true state of the population, and is contrasted with a sample statistic, which is a numerical characteristic or measurement calculated from a sample drawn from the population.

5 Must Know Facts For Your Next Test

1. Population parameters are the true, unknown values that describe the entire population being studied, such as the population mean, population variance, or population proportion.
2. The Finite Population Correction Factor is used to adjust the standard error of the sample mean when the sample size is a significant proportion of the total population size.
3. When the population standard deviation is unknown and the sample size is small, a t-distribution is used to construct a confidence interval for the population mean.
4. A confidence interval for a population proportion is used to estimate the true proportion of the population with a certain characteristic, based on a sample.
5. The sample size required to estimate a population parameter with a specified level of precision and confidence level can be calculated using formulas that depend on the type of parameter being estimated (continuous or binary).

Review Questions

• Explain how the Central Limit Theorem relates to the concept of a population parameter.
  • The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution. This is important for making inferences about population parameters, as it allows us to use the normal distribution to construct confidence intervals and conduct hypothesis tests about the population mean, even when the true population distribution is unknown.
• Describe the role of the Finite Population Correction Factor in the context of population parameters.
  • The Finite Population Correction Factor is used to adjust the standard error of the sample mean when the sample size is a significant proportion of the total population size. This is important because the standard error of the sample mean is typically calculated under the assumption that the sample is drawn from an infinite population. When the sample size is large relative to the population size, the Finite Population Correction Factor is used to account for the fact that the sample is being drawn without replacement, which reduces the variability of the sample mean compared to an infinite population.
• Analyze how the concepts of confidence intervals and sample size calculations relate to the estimation of population parameters.
  • Confidence intervals are used to estimate the true, unknown value of a population parameter based on a sample statistic. The width of the confidence interval depends on the variability of the sample statistic, the desired level of confidence, and the sample size. Similarly, the required sample size to estimate a population parameter with a specified level of precision and confidence level depends on the type of parameter being estimated (continuous or binary), the desired level of precision, and the expected variability in the population. These concepts are crucial for making reliable inferences about population parameters based on sample data.

Related terms

Sample Statistic: A sample statistic is a numerical characteristic or measurement calculated from a sample drawn from the population, and is used to estimate the corresponding population parameter.

Sampling Distribution: The sampling distribution is the probability distribution of a sample statistic, which describes the variability of the statistic across all possible samples that could be drawn from the population.

Central Limit Theorem: The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as the sample size increases.