The efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2 ). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y). Temp. 170 172 173 174 174 175 176 Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04 Temp. 177 180 180 180 180 180 181 Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84 Temp. 181 182 182 182 182 184 184 Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52 Temp. 185 186 188 Ratio 3.00 1.87 3.08 a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features. b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning. c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.
The efficiency ratio for a steel specimen immersed in a
phosphating tank is the weight of the phosphate coating
divided by the metal loss (both in mg/ft2
). The article
“Statistical Process Control of a Phosphate Coating
Line” (Wire J. Intl., May 1997: 78–81) gave the
accompanying data on tank temperature (x) and efficiency ratio (y).
Temp. 170 172 173 174 174 175 176
Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04
Temp. 177 180 180 180 180 180 181
Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84
Temp. 181 182 182 182 182 184 184
Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52
Temp. 185 186 188
Ratio 3.00 1.87 3.08
a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting
features.
b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your
reasoning.
c. Construct a scatterplot of the data. Does it appear
that efficiency ratio could be very well predicted by
the value of temperature? Explain your reasoning.
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