Point Estimate

Definition

A point estimate is a single numerical value that is used to estimate an unknown population parameter, such as the population mean or proportion. It serves as a representative value for the parameter of interest based on a sample drawn from the population.

5 Must Know Facts For Your Next Test

1. A point estimate is the single value obtained from a sample that is used to estimate an unknown population parameter.
2. The accuracy of a point estimate depends on the size of the sample and the variability in the population.
3. Point estimates are used to make inferences about the population, such as in the context of hypothesis testing and confidence interval construction.
4. The sampling distribution of a point estimate, such as the sample mean or proportion, is centered around the true population parameter.
5. The standard error of a point estimate reflects the variability of the estimate and is used to construct confidence intervals around the point estimate.

Review Questions

• Explain how a point estimate is used in the context of a single population mean using the normal distribution (Topic 8.1).
  • In Topic 8.1, which covers a single population mean using the normal distribution, the sample mean $\bar{x}$ is used as a point estimate of the unknown population mean $\mu$. The sample mean is calculated from a random sample drawn from the population and is the best unbiased estimate of the population mean. The accuracy of the point estimate $\bar{x}$ depends on the sample size $n$ and the population standard deviation $\sigma$, which together determine the standard error of the sample mean. This standard error is used to construct a confidence interval around the point estimate, allowing researchers to make inferences about the true population mean.
• Describe how a point estimate is used in the context of a confidence interval for home costs (Topic 8.4).
  • In Topic 8.4, which discusses confidence intervals for home costs, the sample mean home price $\bar{x}$ is used as a point estimate of the unknown population mean home price $\mu$. The point estimate $\bar{x}$ is calculated from a random sample of home prices and is the best available estimate of the true population mean. The standard error of the sample mean is then used to construct a confidence interval around the point estimate, providing a range of plausible values for the true population mean home price. This confidence interval allows researchers to make inferences about the average home cost in the population with a specified level of confidence.
• Analyze how a point estimate is used in the context of a confidence interval for place of birth (Topic 8.5) and women's heights (Topic 8.6).
  • In Topic 8.5, which covers confidence intervals for place of birth, the sample proportion $\hat{p}$ is used as a point estimate of the unknown population proportion $p$. Similarly, in Topic 8.6, which discusses confidence intervals for women's heights, the sample mean $\bar{x}$ is used as a point estimate of the unknown population mean $\mu$. In both cases, the point estimate serves as the best available estimate of the true population parameter based on the sample data. The standard error of the point estimate is then used to construct a confidence interval, which provides a range of plausible values for the true population parameter. These confidence intervals allow researchers to make inferences about the population characteristics, such as the proportion of people born in a certain place or the average height of women, with a specified level of confidence.

Related terms

Sampling Distribution: The probability distribution of a statistic (such as the sample mean or proportion) across all possible samples that could be drawn from a population.

Standard Error: The standard deviation of the sampling distribution of a statistic, which measures the variability of the statistic across repeated samples.

Confidence Interval: A range of values, calculated from a sample, that is likely to contain the true population parameter with a specified level of confidence.