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: n₁ SSB = SST=86362- A Test statistic: Decision: Conclusion: B 5 3 5 364 198 340 Σ.Σ.Χ. =86362 • -(34 SSW = 1090.47-216.67=873.80 Degrees of freedom: Rejection region: C 1204² 17 =1090.47 D 4 302 364² 1982 340², 302² + + + 302²) 3 5 4 Total 17=n 1204 = T 1204² 17 = 216.67

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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:
n₁
SSB =
SST=86362-
A
5
364
(364²
5
Test statistic:
Decision:
Conclusion:
+
Degrees of freedom:
Rejection region:
B
C
ΣΣx = 86362
1204²
17
3
5
198 340
-=1090.47
SSW1090.47-216.67=873.80
D
4
302
198² 340²302²
+
3
Total
17=n
+340² 302²)-1204²-21
5
17
1204 = T
=216.67
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: n₁ SSB = SST=86362- A 5 364 (364² 5 Test statistic: Decision: Conclusion: + Degrees of freedom: Rejection region: B C ΣΣx = 86362 1204² 17 3 5 198 340 -=1090.47 SSW1090.47-216.67=873.80 D 4 302 198² 340²302² + 3 Total 17=n +340² 302²)-1204²-21 5 17 1204 = T =216.67
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