Question

1. The total flow at a wastewater-treatment plant is on average 600 m /day with a standard deviation of 45 m /day and behaves in accordance with a normal distribution. (a) With what probability would the flow on any given day exceed 680 m /day? (b) We can expect to see 90% of the days exhibit a flow above what value? (c) Suppose we wish to test whether the flow mean has changed based on the average taken over 9 randomly selected days. A sample mean X beyond what critical values would make us conclude a change. Assume a Type I error of 0.10? (d) What would be the statistical power of this test against an alternative of 620?

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Answer #1

a) P(X > 680) = P(Z > (680-600)/45) = P(Z>1.7778) = 0.03772

b) Value = Mean + Z10% SD = 600 + 1.282*45 = 657.69

c)

The sample mean corresponding critical value at alpha-5% in two tail is 45 cut points-? Za/2 F-600 1.645 -(575.325, 624.675)

d)

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