Three randomly chosen pieces of four types of PVC pipe of equal wall thickness are tested to determine the burst strength (in pounds per square inch) under three temperature conditions, yielding the results shown below. $$\begin{array} { | c | c | c | c |c | }
\hline{ \text { Temperature } } & \text { PVC1 } & \text { PVC2 } & \text { PVC3 } & \text { PVC4 } \
\hline& 250 & 301 & 235 & 217 \
\text { Hot } \left( 70 ^ { \circ } \mathrm { C } \right) & 273 & 285 & 260 & 255 \
& 281 & 275 & 279 & 241 \
\hline& 321 & 342 & 302 & 240 \
{ \text { Warm } \left( 40 ^ { \circ } \mathrm { C } \right) } & 322 & 322 & 315 & 260 \
& 299 & 339 & 301 & 278 \
\hline & 358 & 375 & 328 & 301 \
\text { Cold } \left( 10 ^ { \circ } \mathrm { C } \right) & 363 & 355 & 336 & 333 \
& 341 & 354 & 342 & 302 \
\hline
\end{array}$$ Which test would be appropriate?
A)One-factor ANOVA
B)Two-factor ANOVA with replication
C)Dependent (paired-samples) t-test
D)Two-factor ANOVA with no replication

Question

Three randomly chosen pieces of four types of PVC pipe of equal wall thickness are tested to determine the burst strength (in pounds per square inch) under three temperature conditions, yielding the results shown below. $$\begin{array} {  | c | c | c | c |c | } 
\hline{ \text { Temperature } } & \text { PVC1 } & \text { PVC2 } & \text { PVC3 } & \text { PVC4 } \
\hline& 250 & 301 & 235 & 217 \
\text { Hot } \left( 70 ^ { \circ } \mathrm { C } \right) & 273 & 285 & 260 & 255 \
& 281 & 275 & 279 & 241 \
 \hline& 321 & 342 & 302 & 240 \
 { \text { Warm } \left( 40 ^ { \circ } \mathrm { C } \right) } & 322 & 322 & 315 & 260 \
& 299 & 339 & 301 & 278 \
\hline & 358 & 375 & 328 & 301 \
\text { Cold } \left( 10 ^ { \circ } \mathrm { C } \right) & 363 & 355 & 336 & 333 \
& 341 & 354 & 342 & 302 \
\hline
\end{array}$$ Which test would be appropriate?
A)One-factor ANOVA
B)Two-factor ANOVA with replication
C)Dependent (paired-samples) t-test
D)Two-factor ANOVA with no replication

Quizplus · Accepted Answer

The data involves testing three randomly chosen pieces of four types of PVC pipes and the burst strength for each type under different temperature conditions. Therefore, this is a two-factor ANOVA with replication, where the factors are the type of PVC pipe and the temperature conditions. Since there are multiple measurements for each combination of factors (three tests for each type of PVC pipe under each temperature condition), replication is present. A one-factor ANOVA would only be appropriate if we were interested in comparing the burst strengths across the different types of PVC pipes, but not across different temperature conditions. A dependent (paired-samples) t-test would only be appropriate if we were interested in comparing the burst strengths before and after some intervention for the same set of PVC pipes. A two-factor ANOVA with no replication would only be appropriate if we had only one set of measurements for each combination of factors.

Three Randomly Chosen Pieces of Four Types of PVC Pipe