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Workers at the Daivik diamond mine in northern Canada extract approximately 1800 DMT (dry metric tons) of ore per day, which is sifted and examined for diamonds. New machinery has just been installed that is designed to increase the amount of ore extracted per day. A random sample of 36 days was selected, and the amount of ore extracted each day was recorded. The sample mean was x^‾= 1852 DMT.

Assume s = 202 DMT.

a. Is there any evidence to suggest the new machinery has improved production? Use a = 0.05.

b. What is the probability of a type II error if the true mean amount of ore extracted has changed to 1875 DMT; that is, find β(1875)? Find the probability of a type II error if the true mean is 1925 DMT.

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