Cerium dioxide (also called ceria) is used in many applications, including pollution control and wastewater treatment. The article “Mechanical Properties of Gelcast Cerium Dioxide from 23 to 1500 °C” (J. Engr. Mater. Technol. 2017) reports an experiment to determine the relationship between y = elastic modulus (GPa) and x = temperature for ceria specimens under certain conditions. A scatterplot in the article suggests a quadratic relationship.

a. The article reports the estimated equation y = −1.92 10⁻⁵x² – .0191x + 89.0. Over what temperature range does elastic modulus increase with temperature, and for what temperature range does it decrease?
b. Predict the elastic modulus of a ceria specimen at 800 °C.
c. The coefficient of determination is reported as R² = .948. Use the fact that the data consisted of n = 28 observations to perform a model utility test at the .01 level.
d. Information consistent with the article suggests that at x = 800, s_Ŷ = 2.9 GPa. Use this to calculate a 95% CI for μ_YΙ800.

e. The residual standard deviation for the quadratic model is roughly s_e = 2.37 GPa. Use this to calculate a 95% PI at x = 800, and interpret this interval.