Principles of Managerial Statistics and Data Science

9Interval Estimation for One Population Parameter

9.1 Introduction

For the most part, we have been assuming the values of the parameters of a distribution are known. Often, we wish to reach managerial decisions, and we can express a problem at hand in terms of an unknown parameter value. By drawing inference on the value of the parameter, we can solve the managerial problem. To perform inference effectively, the best estimator of a parameter among many choices must be used. Chapter 8 covered the properties that help determine what the best estimator for a parameter is. However, once the best estimator is found, it is not enough to get an estimate from it to perform inference.¹

P( = k) = 0 for Any Constant k

Suppose you take a random sample of size 60 from a normally distributed population with mean 10 and standard deviation 2.5. is unknown and inference on its value is needed. We already know that is the best estimator of . Suppose, the sample average turned out to be 8.5. Now, the probability that the sample mean would be 8.5 is zero. So, how did that value happen? The implication ...