We decide to run a test using an experimental evaporation pan and a standard evaporation pan over ten successive days. The two types are set up side-by-side so 238 Statistical Inferences for the Mean that atmospheric conditions should be the same. A coin is tossed to decide which evaporation pan is on the lefthand side and which on the righthand side on any particular day. The measured daily evaporations are as follows: Pair or Day No. 1 2 3 4 5 6 7 8 9 10 Evaporation, mm: Pan A 9.1 4.6 14.0 16.9 11.4 10.7 27.4 22.8 42.8 29.4 Pan B 6.7 3.1 13.8 16.6 12.3 6.5 24.2 20.1 41.9 27.7 d = Agway, A - B 2.4 1.5 0.2 0.3 -0.9 4.2 3.2 2.7 0.9 1.7 Does the experimental Pan A give significantly higher evaporation than the standard Pan B at the 1% level of significance?Two additives to Portland cement are being tested for their effect on the strength of concrete. 21 batches were made with Additive A, and their strengths showed standard deviation s, = 41.3. 16 batches were made with the same percentage of Additive B, and their strengths showed standard deviation s, = 26.2. Assume that the strengths of concrete follow a normal distribution. Is there evidence at the 1% level of signifi- cance that the concrete made with Additive A is more variable than concrete made with Additive B?A mechanical engineer has decided to test a novel heat exchanger in an oil refinery. The major result will be the amount of heating produced in a petroleum stream which varies in composition. Tests will be done at two compositions and three flow rates. To get sufficient precision each combination of composition and flow rate will be tested five times. A factorial design will be used. a) How many tests will be required? b) List all tests. c) How will the order of testing be determined?A civil engineer is planning an experiment to compare the levels of biological oxygen demand (B.O.D.) at three different points in a river. These are just upstream of a sewage plant, five kilometers downstream, and ten kilometers downstream. Assume that in each case samples will be taken in the middle of the stream (in practice samples would likely be taken at several positions across the stream and averaged). One set of samples will be taken at 6 a.m., another will be taken at 2 p.m., and a third will be taken at 10 p.m. The design will block the effect of time of day, as some interfering factors may be different at different times. However, the interaction of these interfering factors with location is expected to be negligible. a) If there is no replication aside from blocking, how many tests are required? b) List all tests. c) Specify which set of tests constitute each block. d) How should the order of tests be determined?Three similar methods of determining the biological oxygen demand of a waste stream are compared. Two technicians who are experienced in this type of work are available, but there is some indication that they obtain different results. A randomized block design is used, in which the blocking factor is the technician. Preliminary examination of residuals shows no systematic trends or other indication of difficulty. Results in parts per million are shown in Table 12.13. Table 12.13: Results of B.O.D. Study in parts per million Method 1 Method 2 Method 3 Technician 1 827 819 847 Technician 2 835 845 867 Is there evidence at the 5% level of significance that one or two methods of determination give higher results than the others
