Chapter 9

Underlying Theory of Statistical Inference

Figure as far as you can, then add judgment.

—Anonymous

The process improvement frameworks use statistical inference, a general methodology that includes several individual tools (such as confidence intervals and hypothesis tests). The theory of statistical inference is used to determine the appropriate formulas for confidence intervals or the hypothesis tests, such as t-tests or F-tests, and it includes the mathematical basis for these formulas.

This chapter will explain some of the key theoretical concepts that underlie statistical inference and explain the concepts of the normal and other probability distributions, sampling distributions, linear combinations, and transformations. This chapter will clarify the methods discussed earlier, so that they will not seem to be conducted in a mysterious “black box” into which one cannot see. Understanding these concepts will prove important in future statistics courses or training.

Why study statistical inference when your goal is to run a start-up? Of course, you do not need to be a mechanical engineer or mechanic to drive a car. Once you learn to use the brake pedal, ignition, steering wheel, and so on, you can drive. You may not see a need to understand the theories behind the combustion engine, distribution of power, or the complexities of the electrical system—you just want the practical skills needed to drive the car. However, if you hear a strange sound from under the hood, ...

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