Suppose that, when setting up the experiment in Problem 1, the operations manager is able...

Suppose that, when setting up the experiment in Problem 1, 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 1, a two-factor factorial design was used, with the first factor, sideto- 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 yarn breaking strength? Discuss.

g. Compare your results in (a) through (f) with those from the completely randomized design in Problem 2. Discuss fully.

Problem 1: An operations manager wants to examine the effect of air-jet pressure (in pounds per square inch [psi]) on the breaking strength of yarn. Three different levels of air-jet pressure are to be considered: 30 psi, 40 psi, and 50 psi. A random sample of 18 yarns are selected from the same batch, and the yarns are randomly assigned, 6 each, to the 3 levels of air-jet pressure. The breaking strength scores are stored in Yarn.

a. Is there evidence of a significant difference in the variances of the breaking strengths for the three air-jet pressures? (Use α = 0.05.)

b. At the 0.05 level of significance, is there evidence of a difference among mean breaking strengths for the three air-jet pressures?

c. If appropriate, use the Tukey-Kramer procedure to determine which air-jet pressures significantly differ with respect to mean breaking strength. (Use α = 0.05.)

d. What should the operations manager conclude?

Problem 2: A student team in a business statistics course performed a factorial experiment to investigate the time required for pain-relief tablets to dissolve in a glass of water. The two factors of interest were brand name (Equate, Kroger, or Alka-Seltzer) and water temperature (hot or cold). The experiment consisted of four replicates for each of the six factor combinations. The following data, stored in PainRelief, show the time a tablet took to dissolve (in seconds) for the 24 tablets used in the experiment:

At the 0.05 level of significance,

a. is there an interaction between brand of pain reliever and water temperature?

b. is there an effect due to brand?

c. is there an effect due to water temperature?

d. Plot the mean dissolving time for each brand for each water temperature.

e. Discuss the results of (a) through (d).