Consider the box compression data presented in Example 11.1. Carry out an analysis of variance F test at significance level .01, and summarize the results in an ANOVA table.

Example 11.1.

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Example 11.1 The article “Compression of Single-Wall Corrugated Shipping Containers Using Fixed and Floating Test Platens" (J. Test. Eval. 1992: 318-320) describes an experiment in which several different types of boxes were compared with respect to compression strength (lb). Table 11.1 presents the results of an experiment involving 1 = 4 types of boxes (the sample means and standard deviations are in good agreement with values given in the article). Table 11.1 The data and summary quantities for Example 11.1 Type of box Compression strength (lb) 1 2 3 4 a 1 2 3 4 b 1 2 3 655.5 721.4 789.2 686.1 737.1 4 671.7 535.1 559.0 400 With ; denoting the true average compression strength for boxes of type i (i = 1, 2, 3, 4), the null hypothesis is Ho: M₁ = M₂ = μ3 = μ4. Figure 11.1a shows a comparative boxplot for the four samples. There is a substantial amount of overlap among observations on the first three box types, but compression strengths for the fourth type appear considerably smaller than for the others. This suggests that Ho is not true. 400 с 1 2 3 4 788.3 679.1 772.5 732.1 639.0 717.2 628.7 586.9 400 500 500 500 600 734.3 699.4 786.9 774.8 696.3 727.1 542.4 520.0 Grand mean = 600 600 700 700 Sample mean 713.00 700 800 800 756.93 800 698.07 562.02 682.50 900 900 Sample SD 46.55 900 40.34 37.20 39.87