In a 1993 study from the British Medical Journal, the researchers compared the n

Question

In a 1993 study from the British Medical Journal, the researchers compared the number of emergency room visits due to car accidents on Friday the 6th and Friday the 13th in order to see if Friday the 13th was a more dangerous time to be out driving. Year and Month 6th 13th 9 13 Oct-89 Jul 90 6 12 Sep 91 11 14 Dec 91 11 10 Mar-92 3 4 Nov 92 5 12 Use a sign test to test whether there is a significant increase (alpha = 0.05) in accidents on the 13th. The original researchers used a paired t test and found a significant increase in the number of accidents. Why might we prefer the t test to our sign test? Why might the sign test be more appropriate in this case?

Explanation / Answer

Sign test of median = 0.00000 versus > 0.00000

N Below Equal Above P Median
13th-6th 6 1 0 5 0.1094 3.500

Conclusion: The estimated p-value is larger than 0.05 level of significance. Hence, we can not reject the null hypothesis and conclude there is not increase in accidents on the 13th.

b) Ans: It is a powerful test with assuming t-distribution and also, it is simple, straightforward, easy to use, and adaptable to a broad range of situations.

c) The sign test is more appropriate in this case because the sample size is not large. So, without assuming any distribution we can apply the sign test.

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