Question

Suppose that you belong to a panel with representatives from the Ministry of the Environment and the Accreditation Services Branch of the Standards Council of Canada. You are responsible for testing scrubbers, i.e. devices to capture carbon dioxide from smokestacks. You do so by measuring how much carbon dioxide they capture in a standard lab setting.

A manufacturer has stated, "When our Scrubber 2 is installed in the standard lab setting, the amount of carbon dioxide captured follows a normal distribution with a mean of more than 800 tons." You are responsible for verifying this. For five different Scrubber 2's, you record the following noisy data indicating the number of tons of carbon dioxide captured:

• 503, 854, 647, 701, 620

Question: Suppose that you're curious as to whether there's a difference between the Scrubber 2 and its predecessor, the Scrubber 1, in terms of the average amount of carbon dioxide captured. For four different Scrubber 1's, you take additional measurements in the standard lab setting:

• 683, 305, 377, 539

Consider the data set of now nine points. You do not wish to assume that either group follows a normal distribution. Would a randomization test be appropriate to assess the difference in means? If yes, run it and report your results. If no, suggest and perform an alternative.

State any assumptions you make.

Answer 1