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1. Consider a manufacturer's claim that bricks produced by a new and more efficient process have a mean compressive strength greater than 50.0 (measured in units of 100 pounds per square inch). Bricks that do not meet this standard are considered nonconforming and will not be used by the customer. From past experience, it is known that the mean compressive strength of bricks is normally distributed with a standard deviation of 6. The bricks will not be accepted unless we can be reasonably sure that the mean is greater than 50.0. A random sample of nine bricks is taken. (a) State the appropriate null and alternative hypotheses. (b) Suppose we use the rejection region { x > 53; to test the null hypothesis. Compute the Type I error probability for the test. Depict the Type I error graphically. (c) Compute the Type II error probability at the alternative u = 55. Depict the Type I error from part (b) and the Type II error graphically. (d) Compute the Type II error probability at the alternative u = 52. Depict the Type I error from part (b) and the Type II error graphically. (e) Find the new critical value (in terms of x) such that the corresponding test has significance level of 0.05. Depict this new significance level and the new critical value graphically