Cyclic adenosine monophosphate (cAMP) is a substance that can mediate cellular response to hormones. In a study of maturation of egg cells in the frog Xenopus laevis, oocytes from each of four females were divided into two batches; one batch was exposed to progesterone and the other was not. After 2 minutes, each batch was assayed for its cAMP content, with the results given in the table.2 There are 24 = 16 possible ways to assign plus and minus signs to the four differences.
(a) For each of the 16 possible results, find the sum of the four differences and the mean difference.
(b) How many of the 16 results yield a mean difference as far from zero as 0.675, the mean difference for the observed data?
(c) Consider testing the null hypothesis that progesterone has no effect on cAMP against the alternative

that progesterone affects cAMP. Considering your results from part (b), what is the P-value for this randomization test, and what conclusions would you draw if α = 0.10?

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cAMP (pmol/oocyte) Frog Control Progesterone d 6.01 2 2.28 3 1.51 2.12 Mean 2.98 SD 2.05 5.23 121 1.40 1.38 2.31 1.95 0.78 1,07 0.11 0.74 0.675 0.40