A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. Let u denote the mean arsenic content for copper treated by this process, and assume that the standard deviation of arsenic content is o = 100 ppm. The sample mean arsenic content x of 75 copper specimens will be computed, and the null hypothesis Ho : 2 1000 will be tested against the alternate H1 : µ < 1000. A decision is made to reject Ho if X < 980. Find the level of this test. a. b. Find the power of the test in part (a) if the true mean content is 965 ppm. For what values of X should H, be rejected so that the power of the test will be 0.95 C. when the true mean content is 965? d. For what values of X should Ho be rejected so that the level of the test will be 5%? e. What is the power of a 5% level test if the true mean content is 965 ppm? f. How large a sample is needed so that a 5% level test has power 0.95 when the true mean content is 965 ppm?

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A copper smelting process is supposed to reduce the arsenic content of the copper to less
than 1000 ppm. Let u denote the mean arsenic content for copper treated by this process,
and assume that the standard deviation of arsenic content is o = 100 ppm. The sample mean
arsenic content x of 75 copper specimens will be computed, and the null hypothesis Ho : 2
1000 will be tested against the alternate H1 : µ < 1000.
A decision is made to reject Ho if X < 980. Find the level of this test.
a.
b.
Find the power of the test in part (a) if the true mean content is 965 ppm.
For what values of X should H, be rejected so that the power of the test will be 0.95
C.
when the true mean content is 965?
d.
For what values of X should Ho be rejected so that the level of the test will be 5%?
e.
What is the power of a 5% level test if the true mean content is 965 ppm?
f.
How large a sample is needed so that a 5% level test has power 0.95 when the true
mean content is 965 ppm?
Transcribed Image Text:A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. Let u denote the mean arsenic content for copper treated by this process, and assume that the standard deviation of arsenic content is o = 100 ppm. The sample mean arsenic content x of 75 copper specimens will be computed, and the null hypothesis Ho : 2 1000 will be tested against the alternate H1 : µ < 1000. A decision is made to reject Ho if X < 980. Find the level of this test. a. b. Find the power of the test in part (a) if the true mean content is 965 ppm. For what values of X should H, be rejected so that the power of the test will be 0.95 C. when the true mean content is 965? d. For what values of X should Ho be rejected so that the level of the test will be 5%? e. What is the power of a 5% level test if the true mean content is 965 ppm? f. How large a sample is needed so that a 5% level test has power 0.95 when the true mean content is 965 ppm?
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