A study was carried out to compare the writing lifetimes of four premium brands of pens (factor A). It was thought that the writing surface (factor B) might affect lifetime, so three different surfaces were randomly selected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., constant pressure and a fixed angle). The accompanying table shows the two lifetimes (min) obtained for each brand-surface combination. Brand of Pen A B AB 1 2 3 4 The hypotheses are as follows. HOG: G² = 0 H₂G: G²>0 Error Total Writing Surface 707, 659 668, 685 659, 685 698, 650 5411 2 713, 726 722, 740 668, 684 704, 666 5623 SS HOA: 1=₂=3 = 4 = 0 HOB: 08² = 0 HaA: at least one a, * 0 HaB: 8² > 0 Carry out an appropriate ANOVA. (Use a = 0.05. Round your answers to two decimal places.) Source df 660, 645 692, 720 678, 750 688, 733 5566 MS XI.. 4110 4227 4124 4139 16,600 Test for an interaction. Find the critical value. (Round your answer to two decimal places.) Fa,1³2

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A study was carried out to compare the writing lifetimes of four premium brands of pens
(factor A). It was thought that the writing surface (factor B) might affect lifetime, so three
different surfaces were randomly selected. A writing machine was used to ensure that
conditions were otherwise homogeneous (e.g., constant pressure and a fixed angle). The
accompanying table shows the two lifetimes (min) obtained for each brand-surface
combination.
A
B
Brand
of Pen
AB
Error
Total
1
2
3
4
=
1
Writing Surface
707, 659
668, 685
659, 685
698, 650
5411
SS
2
713, 726
722, 740
668, 684
704, 666
5623
The hypotheses are as follows.
2=0
HOG: G²
HaG: G² > 0
HOA: α₁ = α₂ = α3 = 4 = 0 HOB: 0B² = 0
HaA: at least one a, # 0
2
HaB: >0
Carry out an appropriate ANOVA. (Use a = 0.05. Round your answers to two decimal places.)
Source df
f
3
660, 645
692, 720
678, 750
688, 733
5566
MS
XI..
4110
4227
4124
4139
16,600
Test for an interaction. Find the critical value. (Round your answer to two decimal places.)
F12
Transcribed Image Text:A study was carried out to compare the writing lifetimes of four premium brands of pens (factor A). It was thought that the writing surface (factor B) might affect lifetime, so three different surfaces were randomly selected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., constant pressure and a fixed angle). The accompanying table shows the two lifetimes (min) obtained for each brand-surface combination. A B Brand of Pen AB Error Total 1 2 3 4 = 1 Writing Surface 707, 659 668, 685 659, 685 698, 650 5411 SS 2 713, 726 722, 740 668, 684 704, 666 5623 The hypotheses are as follows. 2=0 HOG: G² HaG: G² > 0 HOA: α₁ = α₂ = α3 = 4 = 0 HOB: 0B² = 0 HaA: at least one a, # 0 2 HaB: >0 Carry out an appropriate ANOVA. (Use a = 0.05. Round your answers to two decimal places.) Source df f 3 660, 645 692, 720 678, 750 688, 733 5566 MS XI.. 4110 4227 4124 4139 16,600 Test for an interaction. Find the critical value. (Round your answer to two decimal places.) F12
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