In a 2009 study reported in the New England Journal of Medicine, Boyer et al. randomly assigned children aged 6 months to 18 years who had nonlethal scorpion stings to receive an experimental antivenom or a placebo. “Good” results were no symptoms after four hours and no detectable plasma venom.

The alternative hypothesis is that the antivenom leads to improvement. The p-value for a one-tailed Fisher’s Exact Test with these data is 0.009.

a. Suppose the study had turned out differently, as in the following table.

Would Fisher’s Exact Test have led to a p-value larger or smaller than 0.009? Explain.

b. Suppose the study had turned out differently, as in the following table.

Would Fisher’s Exact Test have led to a p-value larger or smaller than 0.009? Explain.

c. Try the two tests, and report the p-values. Were you right? Search for a Fisher’s Exact Test calculator on the Internet, and use it.

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Antivenom Placebo Total No Improvement 1 6. 7 Improvement 7 1 8 Total 7 15