# solution

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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 days.9 Here are the readings given by the detectors:

DATA FILE

91.9\$1rn \$1rn Â 97.8\$1rn\$1rn 111.4\$1rn \$1rn \$1rn 122.3\$1rn \$1rn \$1rn 105.4\$1rn \$1rn\$1rn 95.0

103.8\$1rn \$1rn 99.6\$1rn \$1rn Â Â 96.6\$1rn \$1rn\$1rn 119.3\$1rn \$1rn\$1rn 104.8\$1rn \$1rn\$1rn 101.7

Assume (unrealistically) that you know that the standard deviation of readings for all detectors of this type is Ïƒ = 9.

(a) Give a 95% confidence interval for the mean reading Î¼ 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).

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