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Statistics in Engineering and Science

the distinction between samples and populations,

role of statistics in engineering and scientific

experimentation

relating sample statistics to populations parameters

Mathematical and Statistical Models

research is important in laboratories of industrial manufacturers

Better products are initiated in academic and industrial research laboratories.

All the activities needed to design a product need experimentation and collection of data

The problem-solving

process involves a degree of uncertainty through the natural variation of results

that occurs in virtually all experimental work.

two types of studies

experimental

observational

variables of interest

cannot be controlled, but they can be recorded and analyzed.

variables of interest

often can be controlled and fixed

In most industrial processes there are numerous sources of possible variation.

three basic categories: project planning, experimental

design, and data analysis.

A sample is a group of observations taken from a population or a process.

All possible items or units that determine an outcome of a well-defined

experiment are collectively called a “population”

A simple random sample may be

used to provide observations from which to estimate the population model.

A process is a repeatable series of actions that results in an observable

characteristic or measurement.

Variable. A property or characteristic on which information is obtained in an

experiment.

Response Variable. Any outcome or result of an experiment.

Factors. Controllable experimental variables that can influence the observed values

of response variables.

A convenience

sample is one that is chosen simply by taking observations that

are easily or inexpensively obtained.

Another sampling technique is judgmental sampling, used to select representative observations from a population of interest.

A parameter is a numerical characteristic of a population

or a process. A statistic is a numerical characteristic that is computed from a

sample of observations.

such as µ for the mean and

σ for the standard deviation

The term distribution is used to

refer to the possible values of a variable along with some measure of how

frequently they occur.

A sampling distribution is a theoretical model that describes

the probability of obtaining the possible values of a sample statistic.

A model is termed mathematical if it is derived from theoretical

or mechanistic considerations that represent exact, error-free assumed

relationships among the variables.

A model is termed statistical if it is derived from data that are

subject to various types of specification, observation, experimental, and/or measurement

errors.