Refer to Exercise 6.40. The state regulators also need to obtain a precise estimate of the mean reduction in the pollution level after installing the scrubbers. What sample size is needed to obtain a 99% confidence interval having width of 8.5 ppm?

Exercise 6.40

An environmental impact study was performed in a small state to determine the effectiveness of scrubbers on the amount of pollution coming from the cooling towers of a chemical plant. The amounts of pollution (in ppm) detected from the cooling towers before and after the scrubbers were installed are given below for 23 cooling towers.

Suppose a larger study is planned for a state with a more extreme pollution problem.

a. How many chemical plant cooling towers need to be measured if we want a probability of .90 of detecting a mean reduction in pollution of 10 ppm due to installing the scrubbers using an a  .01 test?

b. What assumptions did you make in part (a) in order to compute the sample size?

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