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	7	14	14
	11	18	18
System 2	10	16	19
	14	18	25

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

Answer 1

using excel data analysis tool for two way anova,following output is obtained..

Anova: Two-Factor With Replication
SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	18	32	32	82
Average	9	16	16	13.667
Variance	8	8	8	17.867
System 2
Count	2	2	2	6
Sum	24	34	44	102
Average	12	17	22	17
Variance	8	2	18	25.6
Total
Count	4	4	4
Sum	42	66	76
Average	10.5	16.5	19
Variance	8.333	3.667	20.667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
factoe A	33.33	1	33.33	3.85	0.0975	5.99
factor B	152.67	2	76.33	8.81	0.0164	5.14
Interaction	12.67	2	6.33	0.73	0.5200	5.14
error	52.00	6	8.67
Total	250.67	11

since p-value for factor A =0.0975>0.05,test is not significant

since ,p-value for factor B =0.0164<0.05,it is significant

since p-value for interaction =0.5200>0.05, test is not significant