The Following Table Shows the Results from a Study to See

Essay

The following table shows the results from a study to see if a home remedy salve for bee stings worked better than a placebo. Each participant was randomly assigned to receive the home remedy salve or a placebo ointment. "Improvement" means that there were no symptoms of pain after fifteen minutes. Home $\begin{array} { c c c } \text { Remedy } & \text { Placebo } & \text { Total } \\ 2 & 1 & 3 \\ 6 & 7 & 13 \\ 8 & 8 & 16 \end{array}$ The alternative hypothesis is that the home remedy salve leads to improvement (in this case, no pain). The p-value for a one-tailed Fisher's Exact Test with these data is $0.500$ . Suppose the study had turned out differently, as in the following table. $\begin{array} { l c c c } & \begin{array} { c } \text { Home } \\ \text { Remedy } \end{array} & \text { Placebo } & \text { Total } \\ \text { No Improvement } & 0 & 3 & 3 \\ \text { Improvement } & 8 & 5 & 13 \\ \text { Total } & 8 & 8 & 16 \end{array}$ Would Fisher's Exact Test have led to a p-value larger or smaller than $0.500$ ?
Explain.