Professor Civiello wishes to investigate problem-solving skills under two conditions: solving a problem with and without background music. In a carefully controlled experiment involving six research participants, Dr. Civiello records the time it takes each participant to solve a problem when background music is being played and the time required to solve a second problem in the presence of "white noise." (Half of the participants receive the music condition first, half the white noise condition first.) The following are the results, in milliseconds:
Using the direct-difference method:
(a) Set up the statistical hypotheses.
(b) Perform the test (α = 05).
(c) Draw final conclusions.