After large Hoods and the consequent large river Hows, 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 How s and vortexes that are generated. After a large flood, the data set in DS 10.6.11 was collected concerning the severity of the scouring around piers of different designs.
(a) Use a goodness of lit test to examine whether there is sufficient 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 p1 be the probability of severe scouring when pier design 1 is used, and let p2, be the probability of severe scouring when pier design 2 is used. Construct a 99'two-sided confidence interval for P1s - P2s.