Many homeowners buy detectors to check for the invisible gas radon in their homes. How accurate are these detectors? To answer this question, university researchers placed 12 radon detectors in a chamber that exposed them to 105 picocuries per liter of radon. The detector readings were as follows:

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

Is there convincing evidence that the mean reading of all detectors of this type differs from the true value 105 picocuries per liter of radon? Carry out a test in detail (*you may assume any required conditions are met but give all other necessary information). State your conclusion.