Two different gauges can be used to measure the depth of bath material in a Hall cell used in smelting aluminum. Each gauge is used once in 15 cells by the same operator.

(a) State any assumptions necessary to test the claim that both gauges produce the same mean bath depth readings. Check those assumptions for which you have the information.
(b) Apply an appropriate statistical procedure to determine if the data support the claim that the two gauges produce different mean bath depth readings.
(c) Suppose that if the two gauges differ in mean bath depth readings by as much as 1.65 inch, we want the power of the test to be at least 0.8. For a = 0.01, how many cells should have been used?

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Cell Gauge I Gauge 2 Cell Gauge I Gauge 2 46 in. 47 in. 1 52 51 50 53 47 10 45 47 45 11 49 51 4 53 50 12 45 45 49 51 13 47 49 6. 48 48 46 43 14 15 53 54 50 51 8. 56 53