Final answer:
A 1-alpha confidence region for a parameter μ is a range of values that provides an estimate of the true value of μ with a certain level of confidence.
Step-by-step explanation:
A 1-alpha confidence region for a parameter μ is a range of values that is constructed using a statistical method and provides an estimate of the true value of μ with a certain level of confidence.
The term '1-alpha' refers to the confidence level, where alpha is the probability that the confidence region does not contain the true value of μ. The confidence region is typically expressed as an interval or a set of intervals.
For example, a 95% confidence region for μ means that there is a 95% probability that the true value of μ lies within the constructed interval.
The interval is determined based on the sample data and the desired level of confidence. In this case, the 95% confidence interval for μ is given as (1.8, 2.2).
The choice of α determines the width of the interval, reflecting the balance between precision and certainty. Constructing a confidence region involves statistical methods based on data distribution assumptions.
This concept is fundamental in statistical inference, providing a nuanced understanding of parameter uncertainty and aiding decision-making in scientific research.