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In: Statistics and Probability

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 the table below.

Swimmer Velocity (m/s)
Water Guar Syrup
1 0.90 0.93
2 0.92 0.97
3 1.00 0.95
4 1.10 1.14
5 1.20 1.23
6 1.25 1.23
7 1.25 1.27
8 1.30 1.30
9 1.35 1.34
10 1.40 1.42
11 1.40 1.44
12 1.50 1.53
13 1.65 1.59
14 1.70 1.70
15 1.75 1.80
16 1.80 1.77
17 1.80 1.84
18 1.85 1.86
19 1.90 1.89
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 = μwaterμguar 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 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 fail to reject H0. The data 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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