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Benzene is a toxic chemical used in the manufacturing of mechanical chemicals. A manufacturer claims that its exit (effluent) water meets the federal regulation standards with a mean of less than 7980 ppm of benzene. To assess the benzene content of the exit water, 10 independentwater samples were collected and found to have an average of 7906 ppm of benzene. Assume a known standard deviation of 80 ppm and use a significant level of 0.01.
(a) Test the manufacturers claim (i.e., H0: µ 7980 ppm versus H1: µ < 7980 ppm).
(b) What is the probability of type II error (the value) if the true mean is 7920 ppm?
(c) What sample size would be necessary to detect a true mean of 7920 ppm with a probability of at least 0.9?
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