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 0.97 3 1.00 0.95 4 1.10 1.15 5 1.20 1.24 6 1.25 1.24 7 1.25 1.27 8 1.30 1.30 9 1.35 1.32 10 1.40 1.41 11 1.40 1.42 12 1.50 1.54 13 1.65 1.58 14 1.70 1.70 15 1.75 1.80 16 1.80 1.77 17 1.80 1.82 18 1.85 1.89 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 ?d = ?water − ?guar syrup.) State the appropriate null and alternative hypotheses. H0: ?d < 0 Ha: ?d = 0 H0: ?d = 0 Ha: ?d < 0 H0: ?d = 0 Ha: ?d ≠ 0 H0: ?d ≠ 0 Ha: ?d = 0 H0: ?d = 0 Ha: ?d > 0 Find the test statistic and P-value. (Use a table or technology. 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 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 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.

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Description: 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 sec

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	0.97
3	1.00	0.95
4	1.10	1.15
5	1.20	1.24
6	1.25	1.24
7	1.25	1.27
8	1.30	1.30
9	1.35	1.32
10	1.40	1.41
11	1.40	1.42
12	1.50	1.54
13	1.65	1.58
14	1.70	1.70
15	1.75	1.80
16	1.80	1.77
17	1.80	1.82
18	1.85	1.89
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

?_d = ?_water − ?_{guar syrup}.)

State the appropriate null and alternative hypotheses.

H₀: ?_d < 0

H_a: ?_d = 0

H₀: ?_d = 0

H_a: ?_d < 0

H₀: ?_d = 0

H_a: ?_d ≠ 0

H₀: ?_d ≠ 0

H_a: ?_d = 0

H₀: ?_d = 0

H_a: ?_d > 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

P-value=

State the conclusion in the problem context.

We fail to 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 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.

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