A copper smelting process is supposed to reduce the arsenic content of the copper to
Chapter 6, Problem 6(choose chapter or problem)
A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. Let \(\mu\) denote the mean arsenic content for copper treated by this process, and assume that the standard deviation of arsenic content is \(\sigma=100 \mathrm {\ ppm}\). The sample mean arsenic content \(\bar{X}\) of 75 copper specimens will be computed, and the null hypothesis \({H}_{0}: \mu \geq 1000\) will be tested against the alternate \(H_{1}: \mu<1000\).
a. A decision is made to reject \(H_0\) if \(\bar{X} \leq 980\). Find the level of this test.
b. Find the power of the test in part (a) if the true mean content is 965 ppm.
c. For what values of \(\bar{X}\) should \(H_0\) be rejected so that the power of the test will be 0.95 when the true mean content is 965?
d. For what values of \(\bar{X}\) should \(H_0\) 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?
Equation Transcription:
Text Transcription:
mu
sigma=100 ppm
bar{X}
H_0:1000
H_1:<1000
H_0
bar{X}{</=}980
bar{X}
H_0
bar{X}
H_0
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