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Chapter 11: Q22E (page 459)

A study was carried out to compare the writing lifetimes of four premium brands of pens. It was thought that the writing surface might affect lifetime, so three different surfaces were randomly selected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., constant pressure and a fixed angle). The accompanying table shows the two lifetimes (min) obtained for each brand-surface combination.

Carry out an appropriate ANOVA, and state your conclusions.

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Most popular questions from this chapter

In an automated chemical coating process, the speed with which objects on a conveyor belt are passed through a chemical spray (belt speed), the amount of chemical sprayed (spray volume), and the brand of chemical used (brand) are factors that may affect the uniformity of the coating applied. A replicated 23 experiment was conducted in an effort to increase the coating uniformity. In the following table, higher values of the response variable are associated with higher surface uniformity:

Surface Uniformity

The water absorption of two types of mortar used to repair damaged cement was discussed in the article 鈥淧olymer Mortar Composite Matrices for Maintenance-Free, Highly Durable Ferrocement鈥� (J. of Ferrocement, 1984: 337鈥�345). Specimens of ordinary cement mortar (OCM) and polymer cement mortar (PCM) were submerged for varying lengths of time (5, 9, 24, or 48 hours) and water absorption (% by weight) was recorded. With mortar type as factor A (with two levels) and submersion period as factor B (with four levels), three observations were made for each factor level combination. Data included in the article was used to compute the sums of squares, which were SSA 5 322.667, SSB 535.623, SSAB 5 8.557, and SST 5 372.113. Use this information to construct an ANOVA table. Test the appropriate hypotheses at a .05 significance level.

The article 鈥淎n Assessment of the Effects of Treatment, Time, and Heat on the Removal of Erasable Pen Marks from Cotton and Cotton/Polyester Blend Fabrics (J. of Testing and Eval., 1991: 394鈥�397) reports the following sums of squares for the response variable degree of removal of marks:

\(\begin{aligned}{l}SSA = 39.171,SSB = .665,SSC = 21.508, SSAB 51.432,SSAC = 15.953,SSBC = 1.382,\\SSABC = 9.016, and SSE = 115.820\end{aligned}\)Four different laundry treatments, three different types of pen, and six different fabrics were used in the experiment, and there were three observations for each treatment-pen-fabric combination. Perform an analysis of variance using \(\alpha = .01\) for each test, and state your conclusions (assume fixed effects for all three factors).

In an experiment to see whether the amount of coverage of light-blue interior latex paint depends either on the brand of paint or on the brand of roller used, one gallon of each of four brands of paint was applied using each of three brands of roller, resulting in the following data (number of square feet covered)


  1. Construct the ANOVA table. (Hint: The computations can be expedited by subtracting 400 (or any other convenient number) from each observation. This does not affect the final results.)
  2. State and test hypotheses appropriate for deciding whether paint brand has any effect on coverage. Use=.05.
  3. Repeat part (b) for brand of roller.
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Four different coatings are being considered for corrosion protection of metal pipe. The pipe will be buried in three different types of soil. To investigate whether the amount of corrosion depends either on the coating or on the type of soil, 12 pieces of pipe are selected. Each piece is coated with one of the four coatings and buried in one of the three types of soil for a fixed time, after which the amount of corrosion (depth of maximum pits, in .0001 in.) is determined. The data appears in the table.

a. Assuming the validity of the additive model, carry out the ANOVA analysis using an ANOVA table to see whether the amount of corrosion depends on either the type of coating used or the type of soil. Use=.05.

b. Compute\(\hat \mu ,{\hat \alpha _1},{\hat \alpha _2},{\hat \alpha _3},{\hat \alpha _4},{\hat \beta _1},{\hat \beta _2},\;and\;{\hat \beta _3}\)
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