Interval Estimation and Confidence Intervals An interval estimation is a method for finding a range of values that is likely to contain a true parameter...
An interval estimation is a method for finding a range of values that is likely to contain a true parameter of a population. It is used to assess the accuracy of an estimate and to make inferences about the population based on a sample.
Confidence intervals are constructed by adding and subtracting a certain amount of error to the sample mean. The error is a measure of how far off the sample mean is from the population mean. The amount of error to add or subtract is determined by the confidence level, which is the desired level of confidence.
Here's how it works:
Sample mean (x̄): This is the average value of the sample.
Sample standard deviation (s): This measures how spread out the sample is.
Confidence level (c): This is the desired level of confidence, usually 95%.
Error (E): This is the amount of error to add or subtract from the sample mean. It is equal to the critical value from the confidence interval distribution.
Confidence interval: (x̄ ± E).
The confidence interval provides a range of values that is likely to contain the true population parameter with the specified confidence level.
Examples:
Advantages of using confidence intervals:
They provide a measure of the accuracy of an estimate.
They allow us to make inferences about the population based on the sample.
They can be used to construct other statistical measures, such as the sample mean and standard deviation.
Overall, interval estimation and confidence intervals are valuable tools for understanding and making inferences about the parameters of a population.