When a (1 - )100% confidence interval is formed for , what is the probability that the interval will not contain within its limits?
To determine the probability that a (1 - α)100% confidence interval will not contain the parameter within its limits, we need to find α, the significance level, first.
The significance level α is typically set by the researcher and represents the maximum allowed probability of rejecting the null hypothesis when it is true. In other words, α represents the probability of making a Type I error.
For a given confidence interval, the significance level α is equal to 1 minus the confidence level (1 - α = confidence level). For example, if you have a 95% confidence interval, the significance level α would be 1 - 0.95 = 0.05.
So, let's say we have a confidence interval at a 95% confidence level. In this case, the significance level α is 0.05. The probability that the interval will not contain the parameter within its limits is equal to the significance level, which in this case is 0.05 or 5%.
In summary, when a (1 - α)100% confidence interval is formed, the probability that the interval will not contain the parameter within its limits is equal to the significance level α.