A factorial experiment was designed to test for any significant differences in t

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. Spanish 10 14 9 13 Language French 12 16 16 18 Germarn 15 19 18 24 System1 System 2 Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use = .05 a. 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 p-value Factor A 0 0 0 Factor B 228.67 2 114.33 9.03 02 Interaction .13 Error Total

Explanation / Answer

Anova: Two-Factor With Replication SUMMARY spanish French german Total System1 Count 2 2 2 6 Sum 24 28 34 86 Average 12 14 17 14.33333 Variance 8 8 8 9.866667 system2 Count 2 2 2 6 Sum 22 34 42 98 Average 11 17 21 16.33333 Variance 8 2 18 25.86667 Total Count 4 4 4 Sum 46 62 76 Average 11.5 15.5 19 Variance 5.666667 6.333333 14 ANOVA Source of Variation SS df MS F P-value F crit Factor A 12 1 12 1.384615 0.28388 5.987378 Factor B 112.6667 2 56.33333 6.5 0.031491 5.143253 Interaction 14 2 7 0.807692 0.489078 5.143253 Within 52 6 8.666667 Total 190.6667 11

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