Question 16.42

16.42 Home radon detectors.

How accurate are radon detectors of a type sold to homeowners? To answer this question, university researchers placed 12 detectors in a chamber that exposed them to 105 picocuries per liter (pCi/l) of radon.13 The detector readings are as follows:

radon

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

We wonder if the median reading differs significantly from the true value 105.

  1. Graph the data, and comment on skewness and outliers. A rank test is appropriate.

  2. We would like to test hypotheses about the median reading from home radon detectors:

To do this, apply the Wilcoxon signed rank statistic to the differences between the observations and 105. (This is the one-sample version of the test.) What do you conclude?