unbiased and does this goat reveal on every occasion Explain your answer using statistics covered in this chapter 1.11 You correlate a seasonal mean el Nino index against the seasonal anomalies of precipitation at 24 locations in the western USA . Eight of the twenty four locations show a relationship with el Nino that is significant at the 95 %% level . Assuming that each of the 24 locations is independent of the others , what is the probability that this result occurred by chance ? Later you discover that the 24 stations are not independent . Using an objective method , you group the 24 stations into three groupings that are independent of each other . You find that one of these three groupings is significantly related to el Nino . How likely is it that this second result occurred by chance ? Bibliography Bretherton , C. S., M . Widmann , V . P. Dymnikov , J. M. Wallace and I. Blade , 1999 : The effective number of spatial degrees of freedom of a time -varying field . Journal - of-Climate , 12 , 1990 -2009 Howson , C. and P. Urbach , 2006 : Scientific Reasoning : The Bayesian Approach 3rd Ed. Open Court , 470 pp . Huff , Darrell , 1954 : How to Lie with Statistics , Norton , 142 Jaynes , E. T., 2003 : Probability Theory : The Logic of Science . Cambridge University Press , 758 pp - Knight , K ., 2000 : Mathematical statistics . Texts in statistical science , Chapman and Hall /CRC , 481 pp . Larson , R. L. and M. L. Marx , 1986 : An Introduction to Mathematical Statistics and its Applications . 2nd , Prentice -Hall , Englewood Cliffs , N .J., 630 . Leith , C. E., 1973 : The standard error of time -averaged estimates of climatic means . J. Appl . Meteorol ., 12 , 1066 -1069 Mendenhall , W ., D.D. Wackerly , y , and R.L. Sheaffer , 1990 : Mathematical Statistics with Applications , PWS -Kent , Boston , p 688 Panofsky , H. A . and G. W . Brier , 1968 : Some Applications of Statistics to Meteorology Pennsylvania State University , University Park , 224 . Wilks , D. S., 1995 and 2005 : Statistical Methods in the Atmospheric Sciences . Academic Press , San Diego , 467 Zwiers , F. W. and H. von Storch , 1995 : Taking serial correlation into account in tests of the mean . J. Climate , 8, 336 -351