A point estimate is a single numerical value used to represent an unknown population parameter, such as the mean or proportion. It is a statistic calculated from a sample that provides the best guess or estimate of the true population value.
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A point estimate is the single value that best represents the unknown population parameter based on the information provided by a sample.
The accuracy of a point estimate depends on the size of the sample and the variability in the population.
Point estimates are used to construct confidence intervals, which provide a range of plausible values for the population parameter.
In the context of a single population mean using the normal distribution (Section 8.1), the sample mean is the point estimate of the population mean.
For the confidence interval for home costs (Section 8.4), the sample mean is the point estimate of the population mean home cost.
Review Questions
Explain how a point estimate is used to construct a confidence interval for a population parameter.
A point estimate, such as the sample mean, is the single numerical value used to represent an unknown population parameter. This point estimate is then used as the center or midpoint of a confidence interval, which provides a range of plausible values for the true population parameter. The width of the confidence interval depends on the variability in the sample and the desired level of confidence, allowing the researcher to make inferences about the population based on the information provided by the sample.
Describe how the point estimate and sampling distribution are used to determine the margin of error in a confidence interval.
The point estimate, such as the sample mean, is the best guess or estimate of the true population parameter based on the sample data. The sampling distribution of the point estimate, which represents the probability distribution of the statistic across all possible samples, is used to determine the margin of error in the confidence interval. The margin of error is calculated as a multiple of the standard error of the point estimate, which is derived from the sampling distribution. This margin of error is then added and subtracted from the point estimate to create the confidence interval, which represents the range of plausible values for the population parameter.
Analyze how the accuracy and precision of a point estimate can affect the interpretation of a confidence interval for a population parameter.
The accuracy and precision of a point estimate, such as the sample mean, directly impact the interpretation of the corresponding confidence interval. If the point estimate is an accurate representation of the true population parameter, the confidence interval will be centered around the correct value. However, if the point estimate is biased or imprecise due to factors like small sample size or high variability in the population, the confidence interval may not contain the true parameter value, even at the desired level of confidence. The width of the confidence interval is also affected by the precision of the point estimate, with narrower intervals indicating greater precision. Interpreting a confidence interval requires considering both the point estimate and the factors that influence its reliability as an estimate of the unknown population parameter.
Related terms
Sample Statistic: A numerical value calculated from a sample that is used to estimate an unknown population parameter.
The probability distribution of a sample statistic, such as the sample mean or sample proportion, across all possible samples of the same size drawn from a population.