Factor A Factor B Response Level 1 Level 1 64.9 Level 1 Level 1 58.3 Level 1 Lev
ID: 3356649 • Letter: F
Question
Factor A Factor B Response
Level 1 Level 1 64.9
Level 1 Level 1 58.3
Level 1 Level 1 32.9
Level 1 Level 1 59.4
Level 1 Level 2 53.3
Level 1 Level 2 44.2
Level 1 Level 2 46.2
Level 1 Level 2 43.3
Level 1 Level 3 51.9
Level 1 Level 3 61.8
Level 1 Level 3 68.5
Level 1 Level 3 64.8
Level 2 Level 1 50.7
Level 2 Level 1 59.3
Level 2 Level 1 58.1
Level 2 Level 1 33.5
Level 2 Level 2 38.4
Level 2 Level 2 50.7
Level 2 Level 2 41.2
Level 2 Level 2 52.6
Level 2 Level 3 53.1
Level 2 Level 3 57.9
Level 2 Level 3 55.7
Level 2 Level 3 74.4
Assume that the accompanying data come from populations that are normally distributed with the same variance. Complete parts (a) through (d).
a) Determine whether or not there is significant interaction between factor A and factor B. Choose the correct answer below.
There is no significant interaction.
There is significant interaction.
(b) If there is no significant interaction, determine if there is a significant difference in the means for the two levels of factor A.
A.There is no significant difference in means.
B.There is significant interaction.
C.There is a significant difference in means.
If there is no significant interaction, determine if there is a significant difference in the means for the three levels of factor B.
A.There is a significant difference in means.
B.There is no significant difference in means.
C.There is significant interaction.
(c) Draw an interaction plot of the data to support the results of parts (a) and (b). Choose the correct graph below.
(d) If there is a significant difference in the means for the two levels of factor A, use Tukey's test to determine which pairwise means differ using a familywise error rate of
alpha equals 0.05.
Choose the correct answer below.
A.The means of levels 1 and 2 of factor A are significantly different.
B.The means of levels 1 and 3 of factor A are significantly different.
C.The means of levels 2 and 3 of factor A are significantly different.
D.There is no significant difference in means for the two levels of factor A.
If there is a significant difference in the means for the three levels of factor B, use Tukey's test to determine which pairwise means differ using a familywise error rate of alpha equals 0.05.
Choose the correct answer below.
A.The means of levels 2 and 3 of factor B are significantly different.
B.The means of levels 1 and 2 of factor B are significantly different.
C.The means of levels 1 and 3 of factor B are significantly different.
D.There is no significant difference in means for the two levels of factor B.
Explanation / Answer
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 5 915.61 915.61 183.121 1.97020 0.132244
A 1 23.80 23.80 23.800 0.25607 0.618976
B 2 885.00 885.00 442.502 4.76086 0.021896
A*B 2 6.80 6.80 3.402 0.03660 0.964135
Error 18 1673.02 1673.02 92.946
Total 23 2588.63
here p-value of A*B is .96>0.05 hence we can claim that there is no interaction.
a) Determine whether or not there is significant interaction between factor A and factor B. Choose the correct answer below.
There is no significant interaction.
(b) If there is no significant interaction, determine if there is a significant difference in the means for the two levels of factor A.
A.There is no significant difference in means. ( as p-value of factor A is 0.61 > 0.05 hence no effect of factor A)
If there is no significant interaction, determine if there is a significant difference in the means for the three levels of factor B.
A.There is a significant difference in means.( as p-value of factor B is 0.02 < 0.05 hence significant effect of factor A)
(d) If there is a significant difference in the means for the two levels of factor A, use Tukey's test to determine which pairwise means differ using a familywise error rate of
alpha equals 0.05.
Choose the correct answer below.
D.There is no significant difference in means for the two levels of factor A.
If there is a significant difference in the means for the three levels of factor B, use Tukey's test to determine which pairwise means differ using a familywise error rate of alpha equals 0.05.
Choose the correct answer below.
A.The means of levels 2 and 3 of factor B are significantly different.
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = y ~ x)
$x
diff lwr upr p adj
2-1 -5.900 -17.251319 5.451319 0.4053722
3-1 8.875 -2.476319 20.226319 0.1442836
3-2 14.775 3.423681 26.126319 0.0095668
>
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