17 



APPENDIX 2 



DURATION OF SAMPLE 



Assume in the first approach that for the specific locale indicated, one of the wave- 

 height distributions has a mean 



X = 7.76 ft 

 and 



ffj = 5.07 ft 

 Then, by standard statistical procedure, the sample size necessary to obtain a sample mean 

 which differs from the true mean by no more than 5 percent with a confidence coefficient of 

 90 percent can be obtained by solving for n in the equation 



y/n = 



k 



0.05 X 



[17] 



where ^ ^ is the particular abscissa on the "i!" distribution with n defined such that the area 

 under the "^" distribution between jj; /t is 90 percent. By substitution 



1.67 (5.07) 



0.05 (7.76) 



467 



that is approximately 467 independent and random observations are necessary. 



Weather observations are characterized by the lack of independence in successive ob- 

 servations when the time interval between observations is relatively short. The duration of 

 interval necessary to insure independence cannot be determined. If one independent obser- 

 vation can be obtained every 10 days, then by the above calculations, more than 13 years are 

 necessary to obtain a sample fulfilling the stipulated conditions. If 7 days are sufficient, 

 then about 9 years are necessary. 



As another approach, suppose that the means of the wave heights obtained for each 

 year (Table 1, page 10) represent independent observations. In this treatment the statistical 

 "population" is the totality of these independent observations. Basing the following compu- 

 tations on the observed mean values, it is found that n = 1. This implies that 7 years of rather 

 extensive observations are necessary to fulfill the conditions imposed. 



Problem: 



Find the number of samples which are required to make 



L-1 



< 0.05 



[18] 



with a probability of 0.90, where X is the mean of the population and X . is the mean of the 

 ith sample. 



