Question

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

	Language
	Spanish	French	German
System 1	6	11	10
	10	15	14
System 2	5	18	14
	9	20	20

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use  = .05.

1. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is
   1. less than .005
   2. between .005 and .0125
   3. between .0125 and .025
   4. between .025 and .05
   5. greater than .05

1. What is your conclusion with respect to Factor A?
   1. Factor A is significant
   2. Factor A is not significant
      
2. The p-value for Factor B is
   1. less than .005
   2. between .005 and .0125
   3. between .0125 and .025
   4. between .025 and .05
   5. greater than .05
      
      What is your conclusion with respect to Factor B?
      1. Factor B is significant
      2. Factor B is not significant
         
3. The p-value for the interaction of factors A and B is
   1. less than .005
   2. between .005 and .0125
   3. between .0125 and .025
   4. between .025 and .05
   5. greater than .05
      
      What is your conclusion with respect to the interaction of Factors A and B?
      1. The interaction of factors A and B is significant
      2. The interaction of factors A and B is not significant

Answer 1

Anova: Two-Factor With Replication
SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	16	26	24	66
Average	8	13	12	11
Variance	8	8	8	10.4
System 2
Count	2	2	2	6
Sum	14	38	34	86
Average	7	19	17	14.33333
Variance	8	2	18	38.66667
Total
Count	4	4	4
Sum	30	64	58
Average	7.5	16	14.5
Variance	5.666667	15.33333	17
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	33.33333	1	33.33333	3.846154	0.097537994	5.987377607
Factor B	164.6667	2	82.33333	9.5	0.013824	5.14325285
Interaction	28.66667	2	14.33333	1.653846	0.267872232	5.14325285
Error	52	6	8.666667
Total	278.6667	11

a)
p-value of Factor A = 0.0975
greater than 0.05

since p-value > 0.05
Factor A is not significant
b)
p-value of factor B = 0.013824
between 0.0125 and 0.025

since p-value < 0.05
Factor B is significant

c) p-value of Interaction = 0.26787
greater than 0.05

since p-value > 0.05
Interaction is not significant