Fifty-three participants performed a series of tests in which a small zap was delivered to one compass
Fifty-three participants performed a series of tests in which a small “zap” was delivered to one compass point, selected at random, on a joystick in their hand. In one setting, subjects were told to move the joystick in the same direction of the zap; in another setting, they were told to move the joystick in the direction opposite to the zap. A series of trials was performed under each setting, and the number of correct moves under both settings was recorded. (“An Experimental Setup to Test Dual-Joystick Directional Responses to Vibrotactile Stimuli,” IEEE Trans. on Haptics 2018.)
a. The authors performed a Wilcoxon signed-rank test on the paired differences (number correct in same direction minus number correct in opposite direction, which is discrete but won't greatly impact the analysis). The resulting test statistic value was s+ = 695. Test H0:µD = 0 versus Ha:µD ≠ 0 at the .10 significance level using the large-sample version of the test.
b. The same article also explored whether participants would make more correct moves if the “zaps” were instead delivered by a glove they wore while grasping the joystick. Again for n = 53 subjects, the difference (number correct with joystick minus number correct with glove) was computed, and the signedrank test statistic value was s+ = 136. Perform a two-sided large-sample test, and interpret your findings.
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