# hw4 - p-value and give the standard error of your estimate...

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STAT 428 Spring 2010 Homework #4 Feb 26 Homework 4 Due in class on Friday, Mar 5. 1. The following table is the ±rst 6 rows and ±rst 6 columns of the 12 × 12 table recording the month of birth and death for 82 descendants of Queen Victoria (we went over this example in the ±rst lecture). 1 0 0 0 1 2 1 0 0 1 0 0 1 0 0 0 2 1 3 0 2 0 0 0 2 1 1 1 1 1 2 0 0 0 1 0 (a) Implement the exact test on this 6 × 6 table to test the null hypothesis that the row and column variables (birth month and death month) are independent. The p -value for exact test is μ = s T Ω 1 { p ( T ) p ( T 0 ) } p ( T ) . where T 0 is the observed table above, Ω is the set of 6 × 6 contingency tables with the same row sums and column sums as T 0 . Here p ( T ) is p ( T ) 1 p 6 i =1 p 6 j =1 n ij ! , T Ω , where n ij is the ( i, j )-th entry of the table. Use sequential importance sampling to estimate the
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Unformatted text preview: p-value and give the standard error of your estimate. Attached your R code and results. (b) Implement the χ 2 test of independence on this 6 × 6 table (although the classical rules of thumb for validity of the chi-square approximation (minimum 5 per cell) are badly violated here). Compare the p-values in parts (a) and (b). 2. Use the sequential importance sampling algorithm to estimate the total number of 6 × 6 contingency tables with the same row sums and column sums as the 6 × 6 table in Problem 1. Give your estimate and the standard error of your estimate. Attach the R code....
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