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 | 8 | 11 | 15 |
| 12 | 15 | 19 | |
| System 2 | 7 | 12 | 19 |
| 11 | 14 | 25 | |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use .
Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | -value | |
| Factor A | |||||
| Factor B | |||||
| Interaction | |||||
| Error | |||||
| Total |
The p-value for Factor A is
What is your conclusion with respect to Factor A?
The p-value for Factor B is
What is your conclusion with respect to Factor B?
The p-value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
| excel: data-data analysis: 2 way ANOVA with replication |
| Source | SS | df | MS | F | p value |
| factor A | 5.33 | 1 | 5.33 | 0.62 | 0.4626 |
| factor B | 206.00 | 2 | 103.00 | 11.88 | 0.0082 |
| interaction | 20.67 | 2 | 10.33 | 1.19 | 0.3664 |
| error | 52.00 | 6 | 8.67 | ||
| total | 284.00 | 11 |
| p value for factor A is greater than 0.05 |
| factor A is not significant |
| p value for factor B is less than 0.01 |
| factor B is significant |
| p value for the interaction of is greater than 0.05 |
| interaction of factor A and factor B is not significant |
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