Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer Level Packaging Conference. Nov. 3-4, 2005). The failure times of the microchips (in hours) was determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. The researchers want to predict failure time (y) based on solder temperature (x).
a. Construct a scatter plot for the data. What type of relationship, linear or curvilinear, appears to exist between failure time and solder temperature?
b. Fit the model, E(y) = β0 + β1x + β2x2, to the data. Give the least squares prediction equation.
c. Conduct a test to determine if there is upward curvature in the relationship between failure time and solder temperature. (Use α = .05.)
Temperature (°C) Time to Failure (hours)
165 .................................... 200
162 .................................... 200
164 .................................... 1,200
158 .................................... 500
158 .................................... 600
159 .................................... 750
156 .................................... 1.200
157 .................................... 1,500
152 .................................... 500
147 .................................... 500
149 .................................... 1,100
149 .................................... 1,150
142 .................................... 3,500
142 .................................... 3,600
143 .................................... 3,650
133 .................................... 4,200
132 .................................... 4,800
132 .................................... 5,000
134 .................................... 5,200
134 .................................... 5,400
125 .................................... 8,300
123 .................................... 9,700