The Williamsburg Bridge is a suspension bridge that spans the East River, connecting the boroughs of Brooklyn and Manhattan in New York City. An assessment of the strengths of its cables is reported in the article ??Estimating Strength of the Williamsburg Bridge Cables?? (R. Perry, The American Statistician, 2002:211??217). Each suspension cable consists of 7696 wires. From one of the cables, wires were sampled from 128 points. These points came from four locations along the length of the cable (I, II, III, IV). At each location there were eight equally spaced points around the circumference of the cable (A, B, C, D, E, F, G, H). At each of the eight points, wires were sampled from four depths: (1) the external surface of the cable, (2) two inches deep, (3) four inches deep, and (4) seven inches deep (the cable is 9.625 inches in radius). Under assumptions made in the article, it is appropriate to consider this as a two-factor experiment with circumferential position and depth as the factors, and with location providing four replicates for each combination of these factors. The minimum breaking strength (in lbf) is presented in the following table for each of the 128 points.

a. Construct an ANOVA table. You may give ranges for the P-values.

b. Can you conclude that there are interactions between circumferential position and depth? Explain.

c. Can you conclude that the strength varies with circumferential position? Explain.

d. Can you conclude that the strength varies with depth? Explain.

Location Circumference Depth II IV 5980 6780 6550 A 1 6250 5910 5800 A 2 6650 6690 5540 6080 6580 A 3 5390 5690 A 4 6510 6700 5980 B 1 6200 6240 6180 6740 B 6430 6590 6500 6110 B 3 5710 6230 6450 6310 B 4 6510 6600 6250 5660 1 5570 5700 6390 6170 6260 6290 5630 6990 3 6050 6120 6290 5800 4 6390 6540 6590 6620 D D 1 6140 6210 5710 5090 5090 6000 6020 6480 D D 3 4 5280 6300 5650 5410 6650 5730 6050 6320 E 1 4890 4830 5000 6490 E 2 5360 5640 5920 6390 E 3 5600 5500 6250 6510 E 4 6640 6810 5760 5200 F 5920 5300 5670 6200 F 2 5880 5840 7270 5230 F 3 6570 6130 5800 6200 F 4 6120 6430 6100 6370 G 6070 6980 6570 6980 G 2 6180 6340 6830 6260 G 3 6360 6420 6370 6550 4 6340 6380 6480 7020 H 1 5950 5950 6450 5870 2 6180 6560 5730 6550 H H 3 4 6560 6560 6690 6450 6670 6790 6600 6700