To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in a table below. The researchers concluded that swimming in guar syrup does not change swimming speed. (Use a statistical computer package to calculate P.)


Swimmer Velocity (m/s)
Water Guar Syrup
1 0.93 2.00
2 1.11 1.46
3 1.06 1.48
4 1.62 1.10
5 1.27 1.70
6 1.38 1.15
7 1.91 0.96
8 1.60 1.93
9 1.29 1.92
10 1.05 1.43
11 1.76 1.54
12 1.42 1.06
13 1.16 1.33
14 0.92 1.17
15 1.28 1.88
16 1.32 1.43
17 1.08 1.26
18 1.53 1.53
19 1.89 0.97
20 1.84 1.34


t = (Round the answer to two decimal places.)
df =
P = (Round the answer to three decimal places.)
#question..