A multinational firm manufactures several types of 1280 × 1024 LCD displays in several locations. They designed a sampling experiment to analyze the number of pixels per screen that have significant color degradation after 52,560 hours (six years of continuous use) using accelerated life testing. The Excel ANOVA table for their experiment is shown below. Some table entries have been obscured. The response variable (Y) is the number of degraded pixels in a given display. $$\begin{array} { | l | c | c | c | c | }
\hline \text { Source of Variation } & S S & d f & M S & F \
\hline \text { Country of origin } & 202.9 & & 101.45 & 4.163475 \
\hline \text { Display type } & 233.2333 & & 58.30833 & \
\hline \text { Interaction } & 147.7667 & & 18.47084 & \
\hline \text { Error } & 1096.5 & 45 & 24.36667 & \
\hline \text { Total } & 1680.4 & 59 & & \
\hline
\end{array}$$ How many display types were there?
A)1
B)2
C)3
D)5

Question

A multinational firm manufactures several types of 1280 × 1024 LCD displays in several locations. They designed a sampling experiment to analyze the number of pixels per screen that have significant color degradation after 52,560 hours (six years of continuous use) using accelerated life testing. The Excel ANOVA table for their experiment is shown below. Some table entries have been obscured. The response variable (Y) is the number of degraded pixels in a given display. $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source of Variation } & S S & d f & M S & F \
\hline \text { Country of origin } & 202.9 & & 101.45 & 4.163475 \
\hline \text { Display type } & 233.2333 & & 58.30833 & \
\hline \text { Interaction } & 147.7667 & & 18.47084 & \
\hline \text { Error } & 1096.5 & 45 & 24.36667 & \
\hline \text { Total } & 1680.4 & 59 & & \
\hline
\end{array}$$ How many display types were there?
A)1
B)2
C)3
D)5

Quizplus · Accepted Answer

The degrees of freedom (df) for the display type can be calculated by subtracting 1 from the number of display types. Given that the df for the interaction is based on the product of the df for country of origin and display type, and knowing the df for error and total, we can deduce the number of display types. The total df (59) minus the error df (45) gives us 14 df for all factors and their interactions. If we assume there are 3 countries (given by the df for country of origin being 2, which is one less than the number of countries), and if the interaction df is 8 (which is one less than the product of the number of countries and display types), we can deduce that there are 5 display types because 3 (countries) * 5 (display types) - 1 = 14 df for factors and interactions, and 3-1 (for countries) + 5-1 (for display types) + 3*5-1 (for interaction) = 14.

A Multinational Firm Manufactures Several Types of 1280 × 1024