# Statistics for Environmental Engineers

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1.2    Community Environmental Problem. Identify an environmental problem in your community and list the variables (factors) for which data should be collected to better understand this problem. What special properties (nonnormal distribution, nonconstant variance, etc.) do you think data on these variables might have?

1.3    Incomplete Scientific Information. List and briefly discuss three environmental or public health problems where science (including statistics) has not provided all the information that legislators and judges needed (wanted) before having to make a decision.

# 2

## A Brief Review of Statistics

KEY WORDS accuracy, average, bias, central limit effect, confidence interval, degrees of freedom, dot diagram, error, histogram, hypothesis test, independence, mean, noise, normal distribution, parameter, population, precision, probability density function, random variable, sample, significance, standard deviation, statistic, t distribution, t statistic, variance.

It is assumed that the reader has some understanding of the basic statistical concepts and computations. Even so, it may be helpful to briefly review some notations, definitions, and basic concepts.

### Population and Sample

The person who collects a specimen of river water speaks of that specimen as a sample. The chemist, when given this specimen, says that he has a sample to analyze. When people ask, “How many samples shall I collect?” they usually mean, “On how many specimens collected from the population shall we make measurements?” They correctly use “sample” in the context of their discipline. The statistician uses it in another context with a different meaning. The sample is a group of n observations actually available. A population is a very large set of N observations (or data values) from which the sample of n observations can be imagined to have come.

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