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 12 13
13 16 17
System 2 9 15 19
13 17 25
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use = .05.

Answer 1

Answer:

See the attached pictures for answer.

Step-by-step explanation:

See the attached pictures for explanation.

Answer 2

Answer:

Step-by-step explanation:

We have a factorial experiment with Factors A and B, levels a=2, b=3, and n=2 observations.

It's necessary to apply a Two-Factor with replication ANOVA by using Excel or calculating by hand.

1. Sum of Squares could be calculated with the following formulas:

$SS_{T}=\sum\limits^a_{i=1}\sum\limits^b_{j=1}\sum\limits^n_{k=1} {(y_{ijk}-y_{...} ^{2} )}\\SS_{A}=bn\sum\limits^a_{i=1} {(y_{i..}^{2}) -Ny_{...} ^{2} }\\SS_{B}=an\sum\limits^b_{j=1} {(y_{.j.}^{2}) -Ny_{...} ^{2} }\\SS_{AB}=n\sum\limits^a_{i=1}\sum\limits^b_{j=1} {(y_{ij.}^{2}) -Ny_{...} ^{2} -SC_{A} -SC_{B}-SC_{AB}}$

2. Calculate Degrees of Freedom

Factor A: $a-1$

Factor B: $b-1$

Interaction: $(a-1)(b-1)$

Within: $ab(n-1)$

Total: $abn-1$

3. Mean Square:

Factor A:  $MS_{A}=\frac{SS_{A}}{a-1}$

Factor B:  $MS_{B}=\frac{SS_{B}}{b-1}$

Interaction:  $MS_{AB}=\frac{SS_{AB}}{(a-1)(b-1)}$

Within:$MS_{E}=\frac{SS_{E}}{ab(n-1)}$

4. Estimate F and P-value

$F_{A}=\frac{SS_{A} }{SS_{E}}$

$F_{B}=\frac{SS_{B} }{SS_{E}}$

$F_{AB}=\frac{SS_{AB} }{SS_{E}}$

Open the attachment to see the results.

5. Analysis of P-values

Factor A: P-value (0.1280 )>(0.05)

Factor B: P-value (0.0315  )<(0.05)

Interaction: P-value (0.2963   )<(0.05)

P-value of Factor B is less than 0.05, then type of language is insignifficant.

P-value of Factor A and interaction are greater than 0.05, then the translator system and the interaction of both factors are signifficant.

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