Two different gauges can be used to measure the depth of bath material in a Hall

Question

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.

Cell      Gauge1      Gauge2      Cell      Gauge1      Gauge 2
1           46 in.          47in.         9          52              51
2            50               53           10         47              45
3            47               45           11         49              51
4            53               50           12         45              45
5            49               51           13         47              49
6            48               48           14         46              43
7            53               54           15         50              51
8            56               53

(a) State any assumptions necessary to test the claim that bothgauges produce the same mean bath depth readings. Check thoseassumptions for which you have the information.

(b) Apply an appropriate statistical procedure to determine if thedata support the claim that the two gauges produce different meanbath depth readings.

(c) Suppose that if the two gauges differ in mean bath depthreadings by as much as 1.65 inch, we want the power of the test tobe at least 0.8. For alpha=0.01, how many cells should have beenused?

Explanation / Answer

a) From the normal probability plot the data fall along a line andconsequently they appear to follow a normal distribution. 10-46 P-Value: 0.158 A-Squared: 0.518 Anderson-Darling Normality Test N: 15 StDev: 2.06559 Average: 0.133333 -3 -2 -1 0 1 2 3 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability diff Normal Probability Plot b) 1) The parameter of interest is the mean difference in depthusing the two gauges, d 2) H0 : d=0 3) H1 : d0 4) No significance level, calculate a P-value 5) The test statistic is tdsnd0=/ 6) Reject H0 if the P-value is significantly small. 7)d=0133. snd==206515. t00133206515025==../. 8) P-value = 2P(T > 0.25) 2(0.40)

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