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 the table below.
Swimmer | Velocity (m/s) | |
---|---|---|
Water | Guar Syrup | |
1 | 0.90 | 0.94 |
2 | 0.92 | 0.99 |
3 | 1.00 | 0.95 |
4 | 1.10 | 1.15 |
5 | 1.20 | 1.24 |
6 | 1.25 | 1.24 |
7 | 1.25 | 1.29 |
8 | 1.30 | 1.30 |
9 | 1.35 | 1.33 |
10 | 1.40 | 1.42 |
11 | 1.40 | 1.43 |
12 | 1.50 | 1.54 |
13 | 1.65 | 1.58 |
14 | 1.70 | 1.70 |
15 | 1.75 | 1.80 |
16 | 1.80 | 1.79 |
17 | 1.80 | 1.83 |
18 | 1.85 | 1.86 |
19 | 1.90 | 1.88 |
20 | 1.95 | 1.95 |
The researchers concluded that swimming in guar syrup does not change mean swimming speed. Are the given data consistent with this conclusion? Carry out a hypothesis test using a 0.01 significance level. (Use
μd = μwater − μguar syrup.)
State the appropriate null and alternative hypotheses.
H0: μd = 0
Ha: μd > 0
H0: μd = 0
Ha: μd < 0
H0: μd < 0
Ha: μd = 0
H0: μd ≠ 0
Ha: μd = 0
H0: μd = 0
Ha: μd ≠ 0
Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t=P-value =
State the conclusion in the problem context.
We fail to reject H0. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.We reject H0. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed. We reject H0. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.We fail to reject H0. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.
To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a...
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 ud = Uwater -...
State the appropriate null and alternative hypotheses. Find the test statistic and P-value. And State the conclusion in the problem context. To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-billed 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 the table below. Swimmer Velocity (m/s) Water Guar Syrup...
Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this is true for experienced runners. They recorded time to exhaustion for 11 triathleteswhile running on a treadmill at a speed determined to be near their peak running velocity. The time to exhaustion was recorded for each participant on two different days. On one day, each participant ran while listening to music that the runner selected as motivational. On a different...
Many runners believe that listening to music while running enhances their performance. The authors of a paper wondered if this is true for experienced runners. They recorded time to exhaustion for 11 triathletes while running on a treadmill at a speed determined to be near their peak running velocity. The time to exhaustion was recorded for each participant on two different days. On one day, each participant ran while listening to music that the runner selected as motivational. On a...