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	9	10	11
	13	14	15
System 2	8	14	19
	12	16	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

   
   
2. The p-value for Factor A is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 21
   
   What is your conclusion with respect to Factor A?
   SelectFactor A is significantFactor A is not significantItem 22
   
3. The p-value for Factor B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 23
   
   What is your conclusion with respect to Factor B?
   SelectFactor B is significantFactor B is not significantItem 24
   
4. The p-value for the interaction of factors A and B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 25
   
   What is your conclusion with respect to the interaction of Factors A and B?
   SelectThe interaction of factors A and B is significantThe interaction of factors A and B is not significant

Answer 1

For the given data using Anova  two factor with replication in Excel we get output as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	40.33333	1	40.33333	4.653846	0.074356	5.987378
Columns	98.66667	2	49.33333	5.692308	0.041111	5.143253
Interaction	50.66667	2	25.33333	2.923077	0.129934	5.143253
Within	52	6	8.666667
Total	241.6667	11

From the above output