156CHAPTER 6The expected values areEijOiOjO, as shown in the following table.10.299013.350513.35056.95889.02069.02069.742312.628912.6289(b) Theχ2test is appropriate here, since all the expected values are greater than 5.There are 31314 degrees of freedom.χ2∑3i1∑3j1OijEij2Eij6 4808.From theχ2table,P0 10. A computer package givesP0 166.There is no evidence that the rows and columns are not independent.9.(iii) Both row totals and column totals in the observed table must be the same as the row and column totals,respectively, in the expected table.11.Letpi,i0 19 be he probability that a random digit has the valuei. The null hypothesis isH0:pi0 1for alli.The total number of observations isn200. The expected values are equal tonpi200 0 120.The test statistic isχ221202201720220202022018202202520220162022028202201920220222022014202208.There are 1019 degrees of freedom.From theχ2table,P0 10. A computer package givesP0 534.There is no evidence that the random number generator is not working properly.
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