To investigate the fluid mechanics of swimming, twenty swimmerseach swam a specified distance in a water-filled pool and in a poolwhere the water was thickened with food grade guar gum to create asyrup-like consistency. Velocity, in meters per second, wasrecorded and the results are given in the table below.

Swimmer	Velocity(m/s)
Water	GuarSyrup
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 notchange mean swimming speed. Are the given data consistent with thisconclusion? Carry out a hypothesis test using a 0.01 significancelevel. (Use

μ_d =μ_water − μ_{guar syrup}.)

State the appropriate null and alternative hypotheses.

H₀:μ_d = 0

H_a:μ_d > 0

H₀:μ_d ≠ 0

H_a:μ_d = 0

    

H₀:μ_d = 0

H_a:μ_d < 0

H₀:μ_d < 0

H_a:μ_d = 0

H₀:μ_d = 0

H_a:μ_d ≠ 0

Find the test statistic and P-value. (Round your teststatistic to one decimal place and your P-value to threedecimal places.)

t=

P-value=

State the conclusion in the problem context.

We reject H₀. The data do not provideconvincing evidence that swimming in guar syrup changes meanswimming speed.

We fail to reject H₀. The data do notprovide convincing evidence that swimming in guar syrup changesmean swimming speed.   

We fail to reject H₀. The data provideconvincing evidence that swimming in guar syrup changes meanswimming speed.

We reject H₀. The data provide convincingevidence that swimming in guar syrup changes mean swimmingspeed.