Question

# A factorial experiment was designed to test for any significant differences in the time needed to...

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

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