Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 11.1, Problem 5E
In an experiment to assess the effect of the angle of pull on the force required to cause separation in electrical connectors, four different angles (factor A) were used, and each of a sample of five connectors (factor B) was pulled once at each angle (“A Mixed Model Factorial Experiment in Testing Electrical Connectors,” Industrial Quality Control, 1960: 12–16). The data appears in the accompanying table.
| B | ||||||
| 1 | 2 | 3 | 4 | 5 | ||
| A | 0° | 45.3 | 42.2 | 39.6 | 36.8 | 45.8 |
| 2° | 44.1 | 44.1 | 38.4 | 38.0 | 47.2 | |
| 4° | 42.7 | 42.7 | 42.6 | 42.2 | 48.9 | |
| 6° | 43.5 | 45.8 | 47.9 | 37.9 | 56.4 | |
Does the data suggest that true average separation force is affected by the angle of pull? State and test the appropriate hypotheses at level .01 by first constructing an ANOVA table (SST = 396.13, SSA = 58.16, and SSB = 246.97).
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In an experiment to assess the effect of the angle of pull on the force required to cause separation in electrical connectors, four different angles (factor A) were used, and each of a sample of five
connectors (factor B) was pulled once at each angle. The data appears in the accompanying table.
A
0°
20
4°
6°
Ho: B1 = B₂ = ß3 =B4 = ß5 = 0
H₂: no B₁ = 0
Source
ⒸH₂: α₁ = α₂ = x3 = α4 = 0
H₂: no α₁ = 0
0 Ho: a1 = 02 = az = 04 = 0
H: at least one a, # 0
A
B
Error
Total
1
45.2
44.3
42.5
43.9
Does the data suggest that true average separation force is affected by the angle of pull? State the appropriate hypotheses.
Ho: P₁ = B₂ = B3 =B4 = ß5 = 0
H₂: at least one ß, * 0
df
2
42.2
44.5
42.5
45.9
Test the hypotheses at level 0.01 by first constructing an ANOVA table (SST= 397.02, SSA= 54.44, and SSB 250.80). (Round your answers to two decimal places.)
F0.01
SS
B
3
39.7
38.5
42.5
47.6
MS
4
36.7
38.0
42.4
37.5
f
5
45.8
47.5
48.7
56.3
State the conclusion in the problem context.
Reject H. The data…
Chapter 11 Solutions
Probability and Statistics for Engineering and the Sciences
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