solution

 

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:

DATADATA

DATADATADATA

DATADATADATADATADATA

DATADATADATADATADATA

DATADATADATADATADATA

DATADATADATADATADATA

DATADATADATADATADATA

DATADATADATADATADATA

DATADATADATA

DATADATADATADATADATA

DATA FILE

RADON

91.9$1rn $1rn  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   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 σ = 9.

(a) Give a 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).

 

 
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