To investigate the fluid mechanics of swimming, twenty swimmers each swam a spec
ID: 2947673 • Letter: T
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 1.75 1.33 2 1.96 0.95 3 2.00 1.55 4 1.05 0.93 5 1.69 1.14 6 0.93 1.77 7 1.80 0.90 8 1.70 1.27 9 1.07 1.74 10 1.89 1.34 11 1.72 1.68 12 1.73 1.45 13 1.01 1.34 14 1.19 1.87 15 1.34 1.39 16 1.47 1.08 17 1.75 1.78 18 1.61 1.69 19 1.55 1.98 20 1.96 1.20Explanation / Answer
Result:
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.)
t
= 1.18
df
= 19
P
= 0.254
Paired t Test
Data
Hypothesized Mean Difference
0
Level of significance
0.05
Intermediate Calculations
Sample Size
20
DBar
0.1395
Degrees of Freedom
19
SD
0.5309
Standard Error
0.1187
t Test Statistic
1.1752
Two-Tail Test
Lower Critical Value
-2.0930
Upper Critical Value
2.0930
p-Value
0.2544
Do not reject the null hypothesis
t
= 1.18
df
= 19
P
= 0.254
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