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 the P-value to three decimal places.)

Swimmer Velocity (m/s) Water Guar Syrup 1 1.72 1.93 2 1.35 1.41 3 0.97 1.22 4 1.88 1.95 5 1.23 1.91 6 1.28 1.07 7 1.26 1.71 8 1.30 1.25 9 1.81 0.91 10 1.80 1.88 11 1.03 1.49 12 1.83 0.92 13 1.77 1.13 14 0.99 1.04 15 1.23 2.00 16 1.98 1.18 17 1.37 1.17 18 1.50 1.31 19 1.93 1.52 20 1.31 1.11

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Water and Guar Syrup
H0 : D = 0
HA : D 0
Hypothesis test results:

Hence,

t = 0.66

df = 19

p - value = 0.520

Difference Mean Std. Err. DF T-Stat P-value Water - Guar Syrup 0.0715 0.10893812 19 0.65633593 0.5195

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