Consider a permutation test of the null hypothesis that there is no effect of the mutagen, i.e. that the mean number of microsatellite nuclei is the same in the two groups. We will use the difference in means (dose of 80 mg/ml - control) as our test statistic. So, a positive value for the test statistic indicates that the 80 mg/ml dose had a larger number of microsatellite nuclei. The observed difference (calculated from the data above) is 8.2 There are a total of 126 permutations of 9 things into a group of 4 and group of 5. The 126 values of the test statistic (difference in means as dose - no), sorted from smallest to largest, are: -9.35 -8.9 -8 -8 -8 -8 -8 -7.1 -7.1 -7.1 -7.1 -6.65 -6.65 -6.65 -6.65 -5.75 -5.75 -5.75 -5.75 -5.75 -5.75 -5.3 -4.4 -4.4 -4.4 -4.4 -3.95 -3.95 -3.95 -3.95 -3.05 -3.05 -3.05 -3.05 -3.05 -3.05 -3.05 -3.05 -3.05 -3.05 -2.15 -2.15 -2.15 -2.15 -2.15 -2.15 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.25 -0.8 -0.8 -0.8 -0.8 -0.35 -0.35 -0.35 -0.35 0.1 0.1 0.1 0.1 1 1 1 1 1 1 1 1 1 1 1 1.9 1.9 1.9 1.9 1.9 1.9 2.35 2.35 2.35 2.35 2.35 2.35 3.25 3.25 3.25 3.25 3.7 3.7 3.7 3.7 4.6 4.6 4.6 4.6 4.6 4.6 5.05 5.05 5.05 5.05 5.05 5.05 5.95 5.95 5.95 5.95 5.95 5.95 5.95 5.95 5.95 5.95 6.85 6.85 6.85 6.85 7.3 7.3 7.3 8.2 a) If the null hypothesis (no difference) is true, what is the probability of 8.2 or a more extreme positive value? b) What is the two-sided p-value for the test of the null hypothesis of no difference?