Professor doom has applied to the town planning board to build a villains lair in a suburban neighborhood. the local residents object that he will emanate mind-control rays from his new home to make neighbors more susceptible to his mental control. however, the town planning board approve his lair and then flee the country with ten million dollars each. a local statistician quickly jumps into action, administering a free will test to a random sample of 11 residents. after the lair is built, he administers the test again to each of the original participants. the scores are as follows: before after the test measures a free will quotient. people under the mental domination of another would receive lower scores. does the statistician have evidence that professor doom is controlling his neighbors? the sample differences (before - after) are: before 80 82 94 87 84 j88 186 [85 88 92 86 after 70 82 86 91 1 81 80 82 81 - 90 85 91 diff the mean of the sample differences is (exact answer): the standard deviation of the sample differences (four places after the decimal) is: the degrees of freedom are df = the test-statistic (type in a positive t; three places after the decimal) is t = using the t-chart, the p-value is between and (exact answers, smaller followed by bigger).