Table 5. Chi-Square "Goodness of Fit" 



Pier No. 



Chi-Square 

 Statistic 



Chi-Square 



Distribution Value 



at the 5% Level 



11 

 12 

 13 

 14 



X = 5.623 

 X = 5.513 

 X = 14.349 

 X = 6.211 



X(0.05,5) = 11.070 

 X(0.05,8) = 15.507 

 X(0.05,10) = 18.307 

 XCO.05,8) = 15.507 



To interpret the results, the Chi-square statistic should be compared 

 with that of the Chi-square distribution value. If the Chi-square statis- 

 tic is lower than the Chi-square distribution value for a given confidence 

 level and number of degrees-of-freedom, then it may be assumed that the data 

 can be characterized by the expected distribution, in this case the normal 

 distribution, at a confidence level of 95 percent. 



If the Chi-square statistic value is larger than the Chi-square distri- 

 bution value, then the assumption that the observed distribution is normal 

 would be rejected. This is because the probability that the actual distri- 

 bution is normal and the difference between the Chi-square values is due to 

 chance is less than 5 percent. 



Since the Chi-square statistic for all four piers is less than the 

 corresponding Chi-square distribution value, the hypothesis that the pile 

 diameters can be characterized by the normal distribution is accepted. 



The purpose of regression analysis is to estimate the effect of one or 

 more variables upon another. When planning an underwater inspection, it is 

 desirable to be able to estimate the time required to perform an inspection 

 based upon the levels of inspection for a given set of piles and bents. 



Table 6 shows the independent and dependent variables listed in rows. 

 The columns contain the values that correspond to these variables. Each 

 column represents one diving session. The data for Pier 12 are not included 

 because of the difference in the diving techniques. For Pier 12, the divers 

 were using surface-supplied air; Piers 11, 13, and 14 were inspected by 

 divers using scuba equipment. 



Table 6. Multiple Regression Analysis (Input) 







Pier 



14 





Pier 



13 



Pier 11 



Variables 















(One 

















Dive 1 



Dive 



2 



Dive 3 



Dive 1 



Dive 2 



(Dive) 



Independent 

 No. of bents 



10 



7 





17 



17 



16 



45 



Level I (no. piles) 



117 



85 





237 



256 



266 



30 



Level II (no. piles) 



85 



49 





90 



89 



53 



114 



Dependent 



Time, min 



125 



65 





144 



165 



150 



143 



34 



