Question

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-billed 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 0.90 0.94 0.92 0.98 0.95 1.15 1.24 1.24 1.25 1.28 1.30 1.35 1.33 1.40 1.42 1.40 1.43 1.50 1.54 1.59 1.65 1.70 1.70 1.75 1.80 1.78 1.80 1.80 1.85 1.83 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. (Used-water - Hauar syrup) State the appropriate null and alternative hypotheses. Ho: Md = 0 Haid < 0 Ho: Moto Haid = 0 Ho Hd = 0 Haud > 0

State the appropriate null and alternative hypotheses.

Find the test statistic and P-value.

And State the conclusion in the problem context.

Answer 1

Solution; Here la velocity of the water swimmer & waterpool lle= velocity of the swimmer ispod and - water was thicked to create a syrup uda ex-l2. a) Hull Hypothesis: Ho: led to Alternative Hypotheses: Huild to b Test stolestie: to Id- hypothesis value नाल Here hypothesis value is o.

Swimmer & velociter (m/s) water sugarsyrup difference d² (d 0.94 -0.04 0.90 0.92 0.98 0.0016 00036 0.0025 1.00 0.95 005 1.10 6.15 -005 0.0025 1.20 -oou 0.0016 0.0001 125 0.01 1,25 1-24 1124 1.28 1130 1-33 -003 1-30 0.00 0.02 0.0009 0.0000 0.0004 1.35 1.40 1.42 -002 0.0004 1-43 1.00 -003 0.0009 1-54 -0.04 O 0016 1.59 0.06 0.0036 1. to 000 0.000 -0.05 Stoon 1.80 1.78 0:02 0.0004 1-83 -0.03 -0.01 1.85 981 0.0009 0.0001 00001 190 0.01 1.89 1.95 1.95 0.00 0.0000 Total -0.23 0.0237 id - Sad -> Foto > -0.0115.

/ols.ܘ- d _ za - za - kr - ܕܘ n- ܛܐܤܘ - 27ܘܘ 2372-c-) - 23ܐܘܘ ܕ __-) ܐ2ܘܝܠܐ ܙܙܘܘܘ< 2ܘܘ ( 223ܘ܂ܘܟ. ܙܣ.ܘ -ܗ܆܇ ]323ܘ ܘܦܗ .;] -coll5 to -0.0115 - 0 Test statistic ܟܒܘܘ.ܘ ܩo33332ܝܘ

=> -1.5541 P. Test statistic to -1.5541) Pralue: Here Q=0.01, de and >> 204 ->19, t= -1.554 Puolue - 0.0683 .. Pualue (0.0683) >0.01. conclusion: So we falled to refect the noll hypothesis Ho. and the result is not significant.