A social psychologist wishes to test the assertion that our attitude toward other people tends to reflect our perception of their attitude toward us. A randomly selected member of each of 12 couples who live together is told (in private) that his or her partner has rated that person at the high end of a 0 to 100 scale of trustworthiness. The other member is told (also in private) that his or her partner has rated that person at the low end of the trustworthiness scale. Each person is then asked to estimate, in turn, the trustworthiness of his or her partner, yielding the following results. (According to the original assertion, the people in the trustworthy condition should give higher ratings than should their partners in the untrustworthy condition.)

(a) Use T to test the null hypothesis at the .01 level.
(b) Specify the approximate p-value for this test result.

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TRUSTWORTHINESS RATINGS TRUSTWORTHY (1) UNTRUSTWORTHY (2) COUPLE 60 30 75 35 50 93 74 47 95 63 20 12 34 63 43 79 56 86 72