A B C D 5280 2 5520 NNEP 3 4160 4 5180 5 4760 5800 5320 8 4600 9 4420 10 5280 11 4180 12 4800 13 5580 14 4900 15 4600 N N P H N N E E N N PANNA ANNA w ww ww ww W N N N N N N N NAPP 16 4480 17 5360 18 6160 19 4460 20 4930 21 5680 22 5500 23 4680 24 5600 25 cementP1 +The data in the file cementP1 . txt, available on Blackboard, represent the results of an experiment to investigate sources of variability in testing the strength (in pounds per square inch) of Portland cement. The cement was 'gauged' (mixed with water and worked for a fixed time) by three different gaugers, and then cast into cubes. Each gauger gauged 8 cubes which were then divided into two sets of 4, for testing by two 'breakers'. Breaker 1 Breaker 2 5280 4760 4160 5320 Gauger 1 5520 5800 5180 4600 4420 5580 4180 4600 Gauger 2 5280 4900 4800 4480 5360 5680 4460 4680 Gauger 3 6160 5500 4930 5600 (a) By fitting linear model to the data, investigate how variability in the test results is influenced by differences between gaugers and between breakers. What is your conclusion? (b) Predict the result of a future test (i.e. a future observation) carried out by gauger 2 and breaker 2, and give a 95% confidence interval for your prediction