Scouring Around Bridge Piers After large oods and the

Chapter 10, Problem 10.7.24

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Scouring Around Bridge Piers After large oods and the consequent large river ows, there can be a reduction in the level of the riverbed around the piers of bridges that is known as scouring. This can be a serious problem if the foundations of the piers become exposed. The amount of scouring can depend on the shape of the pier and the consequent ows and vortexes that are generated. After a large ood, the data set in DS 10.7.11 was collected concerning the severity of the scouring around piers of different designs. (a) Use a goodness of t test to examine whether there is sufcient evidence to conclude that the pier design has any effect on the amount of scouring. (b) Consider pier design 1. Are the data consistent with the contention that for this design the three levels of scouring are all equally likely? (c) Show how to perform a two-sided hypothesis test of whether for pier design 3 the probability of a minimal scour depth is 25%. (d) Let p1s be the probability of severe scouring when pier design 1 is used, and let p2s be the probability of severe scouring when pier design 2 is used. Construct a 99% two-sided condence interval for p1s p2s.