Notes › EENG 3421: Probability and Statistics for Engineers Lecture 25
Estimation and Confidence Intervals
235 words 2 min Modified
Table of Contents
Estimation
- Estimation assigns numerical value or values to a population parameter based on sample information
The assignment of value or values to a population parameter based on a value of the corresponding sample statistic is called estimation
The value assigned to a population parameter based on a sample statistic is called an estimate The sample statistic used to estimate a population parameter is called an estimator
The value of a sample statistic used to estimate a population parameter is called a point estimate
Interval Estimation and Confidence Level
- Interval estimation builds an interval around a point estimate
- Margin of error is the amount added and subtracted from the point estimate
Each interval is constructed with regard to a given confidence level and is called a confidence interval The confidence interval is
$$ \text{point estimate} \pm \text{margin of error} $$Confidence level is denoted by $(1-\alpha)100\%$ The significance level is $\alpha$
The margin of error for the estimate of $\mu$ is denoted by $E$
$$ E = z\,\sigma_{\bar x} $$Confidence Interval for $\mu$ with $\sigma$ Known
The $(1-\alpha)100\%$ confidence interval for $\mu$ under the normal model is
$$ \bar x \pm z\,\sigma_{\bar x} $$where
$$ \sigma_{\bar x} = \frac{\sigma}{\sqrt n} $$References
- Course lecture slides 23–26
Sources
- Course lecture slides 23–26