To investigate the fluid mechanics of swimming, twenty swimmers each swam a spec

Question

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 the P-value. Use ?water ? ?guar syrup. Round your test statistic to two decimal places and your P-value to three decimal places.)

Swimmer Velocity (m/s) Water Guar Syrup 1 1.81 1.15 2 1.47 1.70 3 1.05 1.81 4 1.39 1.85 5 1.26 1.62 6 1.77 1.93 7 1.78 1.04 8 0.90 1.94 9 1.74 1.91 10 1.42 1.96 11 1.30 1.34 12 1.88 1.82 13 1.97 1.44 14 1.17 1.86 15 1.93 1.86 16 1.21 1.30 17 1.00 1.96 18 1.58 1.62 19 1.11 0.98 20 1.08 1.24

Explanation / Answer

t = ( x1 -x2)/sqrt(s1^2/n1 +s2^2/n2)
= (1.4410 - 1.6165)/sqrt(0.3436^2/20 + 0.3316^2/20)
= -1.6436

df = 20-1 = 19

p value = .1168

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