In a test of the effectiveness of a new battery design, 16 battery-powered music boxes are randomly provided with either the old design or the new version. Hours of playing time before battery failure were as follows:
8 boxes, 3.3, 6.4, 3.9, 5.4,
new battery type: 5.1, 4.6, 4.9, 7.2 hrs
8 boxes, 4.2, 2.9, 4.5, 4.9,
old battery type: 5.0, 5.1, 3.2, 4.0 hrs
Assuming normal populations with equal standard deviations, use the 0.05 level to determine whether the new battery could be better than the old design. Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for this test?