# Statistics for Environmental Engineers

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2.3    Randomization. A laboratory receives 200 water specimens from a city water supply each day. This exceeds their capacity so they randomly select 20 per day for analysis. Explain how you would select the sample of n = 20 water specimens.

2.4    Experimental Errors. The measured concentration of phosphorus (P) for n = 20 identical specimens of wastewater with known concentration of 2 mg/L are:

1.8 2.2    2.1    2.3    2.1    2.2    2.1    2.1    1.8    1.9

2.4 2.0    1.9    1.9    2.2    2.3    2.2 2.3    2.1    2.2

Calculate the    experimental    errors. Are    the    errors    random?    Plot    the errors    to show their

distribution.

2.5    Summary Statistics. For the phosphorus data in Exercise 2.4, calculate the average, variance, and standard deviation. The average and standard deviation are estimated with how many degrees of freedom?

2.6    Bias and Precision. What are the precision and bias of the phosphorus data in Exercise 2.4?

2.7    Concepts III. Define reproducibility and repeatability. Give an example to explain each. Which of these properties is more important to the user of data from a laboratory?

2.8    Concepts IV. Define normality, randomness, and independence in sampled data. Sketch plots of “data” to illustrate the presence and lack of each characteristic.

2.9    Normal Distribution. Sketch the normal distribution for a population that has a mean of 20 and standard deviation of 2.

2.10    Normal Probabilities. What is the probability that the standard normal deviate z is less than 3; that is, P(z < 3.0)? What is the probability that the absolute value of z is less than 2; that is, P(|z| < 2)? What is the probability that z > 2.2?

2.11    t Probabilities. What is the probability that t < 3 for v = 4 degrees of freedom; that is, P(t < 3.0)? What is the probability that the absolute value t is less than 2 for v = 30; that is, P(|t | < 2)? What is the probability that t > 6.2 for v = 2?

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