Question

o 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 ?water ? ?guar syrup. Round your test statistic to two decimal places and the P-value to three decimal places.)

Swimmer Velocity (m/s) Water Guar Syrup 1 1.23 1.52 2 1.13 1.33 3 1.82 1.91 4 1.56 1.56 5 1.00 1.90 6 1.45 1.80 7 1.93 1.38 8 1.14 1.24 9 1.74 1.85 10 1.14 1.82 11 0.97 1.29 12 1.52 1.57 13 1.91 1.09 14 1.11 1.30 15 1.66 1.70 16 0.94 1.12 17 1.69 1.29 18 1.25 1.10 19 1.37 1.17 20 1.61 1.51

t = 0.09 Incorrect: Your answer is incorrect.

df = 19 Correct: Your answer is correct.

P = .500 Incorrect: Your answer is incorrect.

Answer 1

Null Hypothesis , the swimming speed does not change

Alternate Hypothesis , swimming speed change in guar syrup

Th calculation table is given below

Swimmer	Water	Guar	d =water-guar	d^2
1	1.23	1.52	-0.29	0.0841
2	1.13	1.33	-0.2	0.04
3	1.82	1.91	-0.09	0.0081
4	1.56	1.56	0	0
5	1	1.9	-0.9	0.81
6	1.45	1.8	-0.35	0.1225
7	1.93	1.38	0.55	0.3025
8	1.14	1.24	-0.1	0.01
9	1.74	1.85	-0.11	0.0121
10	1.14	1.82	-0.68	0.4624
11	0.97	1.29	-0.32	0.1024
12	1.52	1.57	-0.05	0.0025
13	1.91	1.09	0.82	0.6724
14	1.11	1.3	-0.19	0.0361
15	1.66	1.7	-0.04	0.0016
16	0.94	1.12	-0.18	0.0324
17	1.69	1.29	0.4	0.16
18	1.25	1.1	0.15	0.0225
19	1.37	1.17	0.2	0.04
20	1.61	1.51	0.1	0.01
		Total	-1.28	2.9316

Under H0, the test statistic is

Degrees of freedom = n-1= 19

The P-Value is 0.4689

Significance level =0.05

Since p value is greater than significance level, we fail to reject H0.

Conclusion : Hence we donot have enough evidence that swimming speed changes in syrup.