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. Velocity (m/s) Water Guar Syrup Swimmer - M₂² M₂-0 ⒸM₂ M₂=O M 1 ⒸM₂₂ 2 3 7 7 ⒸM₂₂-0 7 9 10 12 13 15 16 B M₂ M₂ O ⒸM₂ MO 18 19 20 0.90 1.00 1.10 1.20 1.25 1.35 1.40 1.40 1.50 1.65 1.70 1.75 Lis 1.80 1.85 1.90 1.95 0.91 0.98 0.95 1.21 1.21 1.28 1.30 1.34 1.42 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. (User p State the appropriate null and alternative hypotheses. 1.51 1.59 1.70 1.80 1.78 M 1.84 Ma 1.86 1.89 1.95 Find the test statistic. (Round your answer to two decimal places) to Use technology to find the value. (Round your answer to four decimal places.) P-value- State the conclusion in the problem context. We fall to reject H. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed We reject M. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed. We fall to reject M. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed. We reject M₂. 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 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. Velocity (m/s) Water Guar Syrup Swimmer - M₂² M₂-0 ⒸM₂ M₂=O M 1 ⒸM₂₂ 2 3 7 7 ⒸM₂₂-0 7 9 10 12 13 15 16 B M₂ M₂ O ⒸM₂ MO 18 19 20 0.90 1.00 1.10 1.20 1.25 1.35 1.40 1.40 1.50 1.65 1.70 1.75 Lis 1.80 1.85 1.90 1.95 0.91 0.98 0.95 1.21 1.21 1.28 1.30 1.34 1.42 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. (User p State the appropriate null and alternative hypotheses. 1.51 1.59 1.70 1.80 1.78 M 1.84 Ma 1.86 1.89 1.95 Find the test statistic. (Round your answer to two decimal places) to Use technology to find the value. (Round your answer to four decimal places.) P-value- State the conclusion in the problem context. We fall to reject H. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed We reject M. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed. We fall to reject M. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed. We reject M₂. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Transcribed Image Text: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
O
Ho: Md = 0
Ha: Md > 0
Ho: Md <
Ho: Md = 0
Ha: Md <0
1
Ho: Md 0
H₂: Md = 0
2
3
4
5
6
7
8
Ha: Md = 0
9
10
11
12
13
14
15
16
17
18
19
20
Velocity (m/s)
Water Guar Syrup
0.90
0.92
1.00
1.10
1.20
1.25
1.25
1.30
1.35
1.40
1.40
1.50
1.65
1.70
1.75
1.80
1.80
1.85
1.90
1.95
0.91
0.98
0.95
1.12
1.21
1.21
1.28
1.30
1.34
1.42
1.44
1.51
1.59
1.70
1.80
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 Mwater - Mguar syrup.)
State the appropriate null and alternative hypotheses.
Ho: Md = 0
Hai Hd #0
1.78
1.84
1.86
1.89
1.95
Find the test statistic. (Round your answer to two decimal places.)
t =
Use technology to find the P-value. (Round your answer to four decimal places.)
P-value =
State the conclusion in the problem context.
O We fail to reject Ho. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.
O We reject Ho. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.
O We fail to reject Ho. The data do not provide convincing evidence that swimming in guar syrup changes mean swimming speed.
We reject Ho. The data provide convincing evidence that swimming in guar syrup changes mean swimming speed.
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