# Refer to Exercise 14.31. Suppose that the five pane designs were randomly selected from a…

Refer to Exercise 14.31. Suppose that the five pane designs were randomly selected from a population of pane designs for participation in the study.

a. Obtain the expected mean squares for all sources of variability.

b. Test all relevant sources of variability for significance. Use a  .05.

c. Compare the results obtained here to the results obtained in Exercise 14.31.

d. Does considering the pane design effects to be random effects seem more relevant than considering them to be fixed effects? Explain your answer.

Exercise 14.31

An experiment was conducted to investigate the heat loss for five different designs for commercial thermal panes. The researcher, in order to obtain results that would be applicable throughout most regions of the country, decided to evaluate the panes at five temperatures: 0°F, 20°F, 40°F, 60°F, and 80°F. A sample of 10 panes of each design was obtained. Two panes of each design were randomly assigned to each of the five exterior temperature settings. The interior temperature of the test was controlled at 70°F for all five exterior temperatures. The heat losses associated with the five pane designs are given here.

a. Identify the experimental design and write an appropriate statistical model.

b. Is there a significant difference in the mean heat losses of the five pane designs? Use   .05.

c. Are the differences in the five designs consistent across the five temperatures? Use   .05 and a profile plot in reaching your conclusion.

d. Use Tukey’s W procedure at an   .05 level to compare the mean heat losses for the five pane designs.

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