Problem 15SE

The article. “Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short- Hot-Wire Method” (X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077–1090) reports measurements of the thermal conductivity (in W ∙ m–1 ∙ K–1) and diffusivity of several polymers at several temperatures (in 1000°C). The following table presents results for the thermal conductivity of polycarbonate.

a. Denoting conductivity by y and temperature by x, fit the linear model For each coefficient, test the hypothesis that the coefficient is equal to 0.

b. Fit the quadratic model For each coefficient, test the hypothesis that the coefficient is equal to 0.

c. Fit the cubic model . For each coefficient, test the hypothesis that the coefficient is equal to 0.

d. Fit the quartic model For each coefficient, test the hypothesis that the coefficient is equal to 0.

e. Which of the models in parts (a) through (d) is the most appropriate? Explain.

f. Using the most appropriate model, estimate the conductivity at a temperature of 120°C.

th Tuesday, March 28 • Example 2: Smokers Beliefs About Health Risks Physicians have expressed concern that a majority of smokers do not view themselves as being at increased risk of cancer. A group of physicians offered the results of a study of 735 current smokers selected at random from U.S. households with telephones. Of the 735 smokers surveyed, 44% indicated that they believed they have a higher than average risk of cancer. Do these data suggest that the true pro