An experiment, carried out in a completely randomized design (Devore 1982), to compare the effects of five different plate lengths of 4, 6, 8, 10, and 12 inches on axial stiffness of metal plate-connected trusses used for roof support, yielded the following observations on axial stiffness index

(kips/in.).

Plate length 4 6 8 10 12 309.2 402.1 392.4 346.7 407.4 409.5 347.2 366.2 452.9 441.8 311.0 361.0 351.0 461.4 419.9 326.5 404.5 357.1 433.1 410.7 349.8 331.0 409.9 410.6 473.4 309.7 348.9 367.3 384.2 441.2 316.8 381.7 382.0 362.6 465.8 Apart from the overall differences of the effects of the five plate lengths on axial stiffness, the experimenter was interested in determining whether the mean stiffness index depends linearly on the actual plate length.

This may be done using an appropriate orthogonal polynomial of the means. Prepare and run a SAS program to obtain the output necessary to provide all of the following information. You must extract numbers from the output and write answers on a separate sheet of paper.

a. Assuming the fixed effects one-way classification model for the data, give estimates of μ1, μ2, μ3, μ4, μ5, and σ2.

b. Write down the corresponding analysis of variance table including the p-value. State the hypothesis tested by the F-statistic and your decision based on the p-value.

c. Use a contrast statement to compute an F-statistic for testing whether the mean stiffness index is linearly related to the plate length. Include the corresponding sum of squares and the F-statistic in an expanded ANOVA table. Based on the p-values, summarize your conclusions.

d. Include an estimate statement for the same comparison as in part

(c). If the mean stiffness index is shown to have a straight-line relationship with the plate length, then estimate the slope of this line by the estimated value of the comparison divided by the sum of squares of its coefficients. Interpret this slope as an increase or decrease of axial index per inch of plate length.