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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?
The uniform steel shaft has two gears attached to it at B and C, two frictionless bearings, and the motor. The motor generates 15kip·in and the gears consume 10kip·in and 5kip·in. Find the diameter of the shaft if the maximum rotation between A an..
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