Question: Radon is a colorless, odorless gas that is naturally 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. Here are the readings given by the detectors. (data provided by Diana Schellenberg, Purdue University School of Health Sciences.)

91.9, 97.8, 111.4, 122.3, 105.4, 95.0, 103.8, 99.6, 96.6, 119.3, 104.8, 101.7

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

a) give a 95% confidence interval for the mean reading \(\mu \) 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).