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 1.71 1.09 2 1.51 1.79 3 1.29 1.13 4 1.73 1.59 5 1.33 0.94 6 1.48 1.52 7 1.09 1.69 8 1.35 0.97 9 1.01 1.35 10 1.46 1.64 11 1.08 0.90 12 1.72 1.62 13 1.33 0.91 14 1.35 0.93 15 0.92 1.75 16 1.34 1.39 17 1.12 1.71 18 1.73 1.84 19 1.53 1.91 20 1.70 1.55

Explanation / Answer

The samples are dependent so we will use paired t - test here.

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 = -0.25

Df = 19

p - value = 0.805

Difference Mean Std. Err. DF T-Stat P-value Water - Guar Syrup -0.022 0.087631405 19 -0.25105155 0.8045

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