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sampling distribution of the test statistic for Fisher’s test

• sampling distribution of the test statistic for Fisher’s test
• Sarah performs a CRD with a dichotomous response and obtains the following data. Treatment S F Total 1 a b 18 2 c d 12 Total 8 22 30 Next, she obtains the sampling distribution of the test statistic for Fisher’s test for her data; it is given below. x P(X = x) P(X ≤ x) P(X ≥ x) −0.6667 0.0001 0.0001 1.0000 −0.5278 0.0024 0.0025 0.9999 −0.3889 0.0242 0.0267 0.9975 −0.2500 0.1104 0.1371 0.9733 −0.1111 0.2588 0.3959 0.8629 0.0278 0.3220 0.7179 0.6041 0.1667 0.2094 0.9273 0.2821 0.3056 0.0652 0.9925 0.0727 0.4444 0.0075 1.0000 0.0075 (a) Find the P-value for the first alternative (p1 > p2) if a = 6. (b) Find the P-value for the third alternative (p1 6= p2) if x = −0.2500. (c) Determine both the P-value and x that satisfy the following condition: The data are statistically significant but not highly statistically significant for the second alternative (p1 < p2).

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