Three checkout lines at a supermarket use three different scanner systems that read the UPC symbols on products and find the prices. The store manager suspects that the three scanner systems have different efficiencies and wants to check their speeds. He measures at randomly selected times the speed of each system in number of items scanned per minute. The measurements are given in the table below. Assume normal distribution with equal variance for the three systems.

1. Conduct a one-way ANOVA to test the null hypothesis that all three scanner systems have the same average number scanned per minute. Use an α = of 0.05.
After studying the test results, a representative of the manufacturer of one of the three scanner systems remarks that the ANOVA results may be affected by the differing skills of the checkout clerks. The clerks were not the same for all measurements.

Wanting to know the difference in the efficiencies of the clerks as well as the systems, the manager redesigns the experiment to yield measurements for all combinations of five clerks and three systems. The measurements from this experiment are tabulated below. Assume normal distribution with equal variance for all cells.
2. Conduct a two-way ANOVA with the above data. Interpret your findings.

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Scan 3 18 Scan 1 16 15 Scan 2 13 18 12 13 5 15 16 15 15 14 12 14 15 18 14 15 15 14 16 14 19 16 17 14 15 17 Scan 1 Scan 2 Scan 3 Clerk 1 5 15 14 16 18 17 17 14 15 Clerk 2 14 15 13 12 Clerk 3 15 14 16 13 Clerk 4 14 15 16 15 12 15 17 16 13 16 14 13 14 15 17 18 14 15 15 14 18 19 20 17 18 17 20 19 17 16 Clerk 5 15 17 14 13 16 20 18 18 17 16 17 19