Table 2.15 contains results of a study comparing radiation therapy with surgery in treating cancer of the larynx. Some R output follows:

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> fisher.test(matrix(c(21,2,15,3),ncol=2,byrow=TRUE),alternative="two.sided")

p-value = 0.6384

> fisher.test(matrix(c(21,2,15,3),ncol=2,byrow=TRUE),alternative="greater")

p-value = 0.3808

> fisher.test(matrix(c(21,2,15,3),ncol=2,byrow=TRUE),alternative="less")

p-value = 0.8947+

a. Report and interpret the P-value for Fisher’s exact test with (i) Ha: θ > 1, and (ii) Ha: θ = 1.

b. Obtain and interpret the mid P-value for Ha: θ = 1 and find the corresponding confidence interval based on mid P-values. Give advantages of this type of P-value, compared to the ordinary one.