radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. because radon is slightly radioactive, there is some concern that it may be a health hazard. radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. university researchers placed 12 detectors in a chamber where they were exposed to 105 picocuries per liter (pci/l) of radon over 3 years. here are the readings given by the detectors:91.9 97.8 111.4 112.3 105.4 85.0 103.8 89.6 96.6 109.3 104.8 91.7 Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is σ = 9. a. Give the 95% confidence interval for the mean reading μ for this type of detector. b. Is there significant evidence at the 5% level that the mean reading differs from the true value 105? State hypotheses and base a test on your confidence interval from (a). c. Calculate the power of this test against the alternative μ=115.
radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. because radon is slightly radioactive, there is some concern that it may be a health hazard. radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. university researchers placed 12 detectors in a chamber where they were exposed to 105 picocuries per liter (pci/l) of radon over 3 years. here are the readings given by the detectors:91.9 97.8 111.4 112.3 105.4 85.0 103.8 89.6 96.6 109.3 104.8 91.7 Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is σ = 9.
a. Give the 95% confidence interval for the mean reading μ for this type of detector.
b. Is there significant evidence at the 5% level that the mean reading differs from the true value 105? State hypotheses and base a test on your confidence interval from (a).
c. Calculate the power of this test against the alternative μ=115.
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