Question: Air Filters. Tests of effectiveness of r = 5 different operator cab air filtration systems (meant to protect agricultural workers operating large mobile pesticide spraying machines) produced ratios y of outside-cab-particlecounts to inside-cab-particle-counts with summary statistics below. (Large ratios y are good.) Suppose that the variation in the ratios y can be described by a single standard deviation appropriate for any fixed design and that the y values for each design are approximately normally distributed.
(a) Find Sp.
(b) Find 95 % confidence limits for the average ratio for design 4.
(c) Find 95 % confidence limits for the difference between the average ratio for design 4 and the average ratio for design 1 (design 4 minus design 1).
(d) Let μ1, μ2, μ3, μ4, and μ5 be the long run average y for the five designs. Suppose designs 2 and 4 use filters supplied by Company X and designs 3 and 5 use filters supplied by Company Y. Give an L (linear combination of design means) that might be used to compare the performance of the two filter companies.
(e) The numbers in the table above for a given design might summarize multiple measurements on a single prototype or summarize individual measurements on several prototypes. Which of these two possibilities is better in practical terms? Why?