Statistics for Environmental Engineers

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This interval contains n = 8.0, so we conclude that the difference between y and n is not so large that random measurement error should be rejected as a plausible explanation.


This use of a confidence interval is equivalent to making a two-sided test of the null hypothesis, as was done in Example 2.11. Figure 2.13 shows the two-sided 90% and 95% confidence intervals for n

Summary


This chapter has reviewed basic definitions, assumptions, and principles. The key points are listed below.


A sample is a sub-set of a population and consists of a group of n observations taken for analysis. Populations are characterized by parameters, which are usually unknown and unmeasurable because we cannot measure every item in the population. Parameters are estimated by statistics that are calculated from the sample. Statistics are random variables and are characterized by a probability distribution that has a mean and a variance.


All measurements are subject to experimental (measurement) error. Accuracy is a function of both bias and precision. The role of statistics in scientific investigations is to quantify and characterize the error and take it into account when the data are used to make decisions.


Given a normal parent distribution with mean n and variance a2 and for random and independent observations, the sample average y has a normal distribution with mean n and variance a2/n. The sample variance s2 has expected value a2. The statistic t = (y — n)l(sljn) with v = n — 1 degrees of freedom has a t distribution.

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