Question

In a comparison of the cleaning action of four detergents, 17 pieces of white cloth were first soiled with black ink. The cloths were then washed under controlled conditions. Assume that all whiteness readings to be normally distributed with common variance. Whiteness readings, made on the 17 pieces of cloth, are shown below Brand A Brand B Brand C Brand D 40 34 24 47 32 40 26 42 31 25 45 48 27 53 Pengiraan awal adalah seperti berikut: Preliminary computations are as follows i Dengan menggunakan aras keertian a 0.05, uji hipothesis tiada perbezaarn diantara empat jenama dari segi min bacaan keputihan selepas mencuci. Using a level of significance ofa 0.05, test the hypothesis of no difference between the four brands as regards mean whiteness readings after washing [8 markah/marks i) Dengan menggunakan kaedah Tukey T perbandingan berganda, tentukan sabun pencuci manakah yang berbeza (guna a 0.05) Using the Tukey T method of multiple comparisons, detemine which detergents are different (use a- 0.05) [4 markah/marks] Total 20 markah/marks]

Answer 1

i)

The one way ANOVA is performed to test the hypothesis,

Null hypothesis: There no difference in mean.

Alternative hypothesis: There is at least one mean is different.

The test is performed as follow,

The ANOVA table is,

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	1192.451	3	397.4837	9.299258	0.001504
Within Groups	555.6667	13	42.74359
Total	1748.118	16

The above values are obtained below,

From the question, the data values are

	Brand A	Brand B	Brand C	Brand D
	40	34	33	24
	47	32	40	26
	42	14	31	25
	45		48	27
	53		44
Sum =	227	80	196	102
Average =	45.4	26.667	39.2	25.5
20	10407	2376	7890	2606
St. Dev. =	5.03	11.015	7.19	1.291
$SS=\sum_i (X_i-\overline{X})^2$	101.2	242.6667	206.8	5
n =	5	3	5	4

S Swithin 2 SS w thin groups 101-24242 66142o68 55 667 广i 2. 구 748 19 = !748.118 ~ 555-667 - 92. 45 Thu d df Tota SS betwen 3 Ms within hn5s 7 42-74 within Cs Scanned wit CamScanner

4, 국서 Tucksy's HD pot hoc test 744 HSD 밞 14-0146P Group fompoSD nsini'cant 2-8733 significant dffetn ua L12 S3 12. 8 733 CS Scanned with CamScanner