Question

Q5.4. (based on Problem 16.22; page 670) A study measured the sorption rates of three different types of chemical solvents. These solvents are used to clean industrial parts. Independent samples from each type of solvent were tested, and their sorption rates were recorded as a mole percentage in the following table: Aromatics 0.64 0.79 0.82 0.87 0.95 1.05 1.06 1.11 1.15 1.33 Chloroalkanes 0.41 0.57083 091 1.12 1.16 1.43 1.58 Esters Use the Kruskal-Wallis test at the 0.05 level of significance to determine if the chemical solvents differ significantly in sorption rate. marks (2) 0.06 0.06:0.09:0.10 0.17 0.18:0.28:0.3410.43 :0.47:0.51 :0.53 0.55:0.60:0.66 E332:HWs 4 out of 6

Answer 1

using excel add-ins tool PHStat for multiple comparison test-Kruskal-Wallis Rank Test ,

following o/p is obtained...

Sample	Value	Rank		Aeromatics	chloroalkanes	esters
esters	0.06	1.5		0.64	0.41	0.06
esters	0.06	1.5		0.79	0.57	0.06
esters	0.09	3		0.82	0.83	0.09
esters	0.1	4		0.87	0.91	0.1
esters	0.17	5		0.95	1.12	0.17
esters	0.18	6		1.05	1.16	0.18
esters	0.28	7		1.06	1.43	0.28
esters	0.34	8		1.11	1.58	0.34
chloroalkanes	0.41	9		1.15		0.43
esters	0.43	10		1.33		0.47
esters	0.47	11				0.51
esters	0.51	12				0.53
esters	0.53	13				0.55
esters	0.55	14				0.6
chloroalkanes	0.57	15				0.66
esters	0.6	16
Aeromatics	0.64	17
esters	0.66	18
Aeromatics	0.79	19
Aeromatics	0.82	20
chloroalkanes	0.83	21
Aeromatics	0.87	22
chloroalkanes	0.91	23
Aeromatics	0.95	24
Aeromatics	1.05	25
Aeromatics	1.06	26
Aeromatics	1.11	27
chloroalkanes	1.12	28
Aeromatics	1.15	29
chloroalkanes	1.16	30
Aeromatics	1.33	31
chloroalkanes	1.43	32
chloroalkanes	1.58	33

Kruskal-Wallis Rank Test for Differences in Medians
Data
Level of Significance	0.05		Group	Sample Size	Sum of Ranks	Mean Ranks
			Aeromatics	10	240	24
Intermediate Calculations			chloroalkanes	8	191	23.875
Sum of Squared Ranks/Sample Size	11446.79		esters	15	130	8.667
Sum of Sample Sizes	33
Number of Groups	3
Test Result
H Test Statistic	20.4256
Critical Value	5.9915
p-Value	0.0000
Reject the null hypothesis

Ho:chemical solvents do not differ significantly in scorption rate

H1:chemical solvents differ significantly in scorption rate

since, p-value =0.0000<α=0.05, so, reject Ho

there is enough evidence to conclude that chemical solvents differ significantly in scorption rate at α=0.05