Final answer:
The relative efficiency of an estimator ˆμ1 refers to how much information it provides about a parameter relative to another point estimate, typically compared based on their variances. Without specific variance values for both estimators, a numerical comparison is not possible. Efficiency is critical in determining the precision and utility of an estimator in statistical analysis.
Step-by-step explanation:
The question is asking for the relative efficiency of ˆμ1 compared to the most efficient point estimate, which is typically the one with the smallest variance. In statistical terms, the efficiency of an estimator is a measure of how much information it provides about the parameter being estimated relative to an alternative estimator. The most efficient estimator given a class of estimators is the one with the smallest variance because it has the least amount of sampling variability and thus provides the most precise estimate of the parameter.
Since there is no explicit information provided about the alternative point estimate or its variance, it is not possible to give a numerical answer here. However, we can say that if an estimator has a smaller variance than another, it is more efficient. The concept of efficiency is important in the estimation as it helps researchers use data more effectively to make inferences about population parameters, like the population mean μ.
Regarding the confidence intervals mentioned in the question, if they are constructed correctly, 90% of such intervals should indeed contain the population mean μ. A 95% confidence interval provides a range within which we expect the true population mean to fall 95% of the time if the interval is computed from an infinite number of sample means.