The following are the number of speeding tickets issued by 2 police officers on

Question

The following are the number of speeding tickets issued by 2 police officers on 17 days:

7 and 10, 11 and 13, 14 and 14, 11 and 15, 12 and 9, 6 and 10, 9 and 13, 8 and 11, 10 and 11, 11 and 15, 13 and 11, 7 and 10, 8 and 8, 11 and 12, 9 and 14, 10 and 9, 13 and 16. Use the sign test at the 0.05 level of significance to test the null hypothesis that on the average the 2 police officers issue equally many speeding tickets per day against the alternative hypothesis that the second police officer tends to issue more than the first.

Explanation / Answer

signs are: - - 0 - + - - - - - + - 0 - - + - we toss out the two 0's and have 12 - and 3 positive If they are the same we would expect the proportion of positives to be 0.50 So the P-value is binomcdf(15,0.50,3) = 0.018 < 0.05 We reject the null hypothesis; there is evidence the second officer writes more tickets.

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