5.5 In a comparison of the cleaning action of four detergents, 20 pieces of white cloth were first soiled with India ink. The cloths were then washed under controlled conditions with 5 pieces washed by each of the detergents. Unfortunately, three pieces of cloth were 'lost' in the course of the experiment. Whiteness readings, made on the 17 remaining pieces of cloth, are shown below. Detergent A BC D 77 74 73 76 81 66 78 85 61 58 57 77 76 69 64 69 63 Assuming all whiteness readings to be normally distributed with common variance, test the hypothesis, with a = 0.05, of no difference between the four brands as regards mean whiteness readings after washing. Ho: H₂₁: n₁ SST=86362- SSB = A Test statistic: B 5 3 5 364 198 340 Σ.Σ.Χ. =86362 Decision: Conclusion: 1204² 17 Degrees of freedom: Rejection region: C -(364² 198² 340² 302²) + + + 5 3 5 4 SSW1090.47-216.67=873.80 -=1090.47 D 4 302 Total 17=n 1204 = T 1204² 17 -=216.67 (1) (1) (1) દર ર

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5.5
In a comparison of the cleaning action of four detergents, 20 pieces of white cloth were first
soiled with India ink. The cloths were then washed under controlled conditions with 5 pieces
washed by each of the detergents. Unfortunately, three pieces of cloth were 'lost' in the
course of the experiment. Whiteness readings, made on the 17 remaining pieces of cloth,
are shown below. Detergent A BC D 77 74 73 76 81 66 78 85 61 58 57 77 76 69 64 69 63
Assuming all whiteness readings to be normally distributed with common variance, test the
hypothesis, with a = 0.05, of no difference between the four brands as regards mean
whiteness readings after washing.
Ho:
H₁:
n
T
SSB
A
SST=86362-
5
364
-(364
Test statistic:
Decision:
Conclusion:
3
5
198 340
ΣΣx = 86362
B
1204²
17
+
Degrees of freedom:
Rejection region:
C
(364² 198² 340²
+
3
5
=1090.47
SSW1090.47-216.67=873.80
+
D
4
302
302²)-!
4
Total
17=n
1204 = T
1204²
17
= 216.67
(1)
(1)
(1)
ર ર ર
Transcribed Image Text:5.5 In a comparison of the cleaning action of four detergents, 20 pieces of white cloth were first soiled with India ink. The cloths were then washed under controlled conditions with 5 pieces washed by each of the detergents. Unfortunately, three pieces of cloth were 'lost' in the course of the experiment. Whiteness readings, made on the 17 remaining pieces of cloth, are shown below. Detergent A BC D 77 74 73 76 81 66 78 85 61 58 57 77 76 69 64 69 63 Assuming all whiteness readings to be normally distributed with common variance, test the hypothesis, with a = 0.05, of no difference between the four brands as regards mean whiteness readings after washing. Ho: H₁: n T SSB A SST=86362- 5 364 -(364 Test statistic: Decision: Conclusion: 3 5 198 340 ΣΣx = 86362 B 1204² 17 + Degrees of freedom: Rejection region: C (364² 198² 340² + 3 5 =1090.47 SSW1090.47-216.67=873.80 + D 4 302 302²)-! 4 Total 17=n 1204 = T 1204² 17 = 216.67 (1) (1) (1) ર ર ર
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