Suppose that, when setting up the experiment in Problem 11.38, the operations manager is able to study the effect of side-to-side aspect in addition to air-jet pressure. Thus, instead of the one-factor completely randomized design in Problem 11.38, a two-factor factorial design was used, with the first factor, side-to-side aspect, having two levels (nozzle and opposite) and the second factor, air-jet pressure, having three levels (30 psi, 40 psi, and 50 psi). A sample of 18 yarns is randomly assigned, 3 to each of the 6 side-to-side aspect and pressure level combinations. The breaking-strength scores, stored in Yarn. are as follows:

At the 0.05 level of significance,
a. Is there an interaction between side-to-side aspect and air-jet pressure?
b. Is there an effect due to side-to-side aspect?
c. Is there an effect due to air-jet pressure?
d. Plot the mean yarn breaking strength for each level of side-to-side aspect for each level of air-jet pressure.
e. If appropriate, use the Tukey procedure to study differences among the air-jet pressures.
f. On the basis of the results of (a) through (e), what conclusions can you reach concerning yam breaking strength? Discuss.
g. Compare your results in (a) through (f) with those from the completely randomized design in Problem 11.38. Discuss fully.

Air-Jet Pressure Aspect 30 psi 40 psi 50 psi Side-to-Side Nozzle Nozzle Nozzle Opposite Opposite Opposite 25.5 24.8 23.2 24.9 23.7 23.7 26.1 24.4 22.7 24.7 23.6 22.6 24.2 23.3 22.8 23.6 21.4 24.9