Chapter 4 Confidence intervals

The confidence interval of a parameter, introduced in Math104, can be thought of as displaying the range of most plausible values for the parameter.

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  The $100(1-\alpha )$% confidence interval of the parameter $\theta$ contains the true value ${\theta }_0$ with probability $\mathrm{1}\mathrm{-}\alpha$.

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  So, if 100 independent random samples of size $n$ were taken from the population and the $100(1-\alpha )$% confidence interval were calculated for each sample then, on average, $100(1-\alpha )$ of the confidence intervals would contain the true value $\theta$.