Statistics for laboratory scientists II

Homework problems for lecture 2

1. Consider the data in the following table.

   0	1	2	3	4	5	6	7	8	9
   98	99	100	89	107	114	100	112	85	96

   Question: Do these data look like they follow a multinomial distribution with n=1000 and p_i=1/10 for all i? (i.e., do the digits 0-9 look equally likely?)

   Use R to do the following.

   1. Perform a chi-square goodness of fit test, using the appropriate asymptotic approximation to calculate a P-value.
   2. Perform a likelihood ratio test for goodness of fit, using the appropriate asymptotic approximation to calculate a P-value.
   3. If you are keen, use computer simulation to estimate P-values for each of the above
   4. What do you conclude?

2. How would things be different if you observed the following table instead? (Note: the counts are the same, but are in a different order.)

   0	1	2	3	4	5	6	7	8	9
   114	112	107	100	100	99	98	96	89	85

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Last modified: Tue Mar 28 17:52:12 EST 2006