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 ?d = ?water − ?guar syrup. Round your test statistic to two decimal places and your P-value to three decimal places.
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 ?d = ?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 | 1.43 | 1.23 |
| 2 | 1.02 | 1.96 |
| 3 | 1.37 | 1.54 |
| 4 | 1.23 | 1.76 |
| 5 | 1.42 | 1.07 |
| 6 | 1.09 | 1.63 |
| 7 | 1.56 | 1.31 |
| 8 | 1.33 | 1.58 |
| 9 | 1.96 | 1.30 |
| 10 | 1.89 | 1.23 |
| 11 | 1.15 | 1.15 |
| 12 | 1.11 | 2.00 |
| 13 | 1.31 | 1.59 |
| 14 | 1.79 | 1.23 |
| 15 | 1.12 | 1.05 |
| 16 | 1.84 | 1.12 |
| 17 | 1.72 | 1.42 |
| 18 | 1.99 | 1.79 |
| 19 | 1.53 | 1.80 |
| 20 | 0.92 | 1.69 |
| t | = |
| df | = |
| P-value | = |
Is there sufficient evidence to suggest that there is any difference in swimming time between swimming in guar syrup and swimming in water? Carry out a hypothesis test using ? = 0.01 significance level.
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