To decide whether two different types of steel have the same true average fracture toughness values, $n$ specimens of each type are tested, yielding the following results: $$\begin{array} { c c c }
\hline \text { Type } & \text { Sample Average } & \text { Sample St. Dev. } \
\hline 1 & 60.2 & 1.0 \
2 & 60.0 & 1.0 \
\hline
\end{array}$$ Calculate the $P$ -value for the appropriate two-sample $z$ test, assuming that the data was based on $n$ = 100. Then repeat the calculation for $n$ = 400. Is the small p-value for $n$ = 400 indicative of a difference that has practical significance? Would you have been satisfied with just a report of the p-value? Comment briefly.

Question

To decide whether two different types of steel have the same true average fracture toughness values, $n$ specimens of each type are tested, yielding the following results: $$\begin{array} { c c c } 
\hline \text { Type } & \text { Sample Average } & \text { Sample St. Dev. } \
\hline 1 & 60.2 & 1.0 \
2 & 60.0 & 1.0 \
\hline
\end{array}$$ Calculate the $P$ -value for the appropriate two-sample $z$ test, assuming that the data was based on $n$ = 100. Then repeat the calculation for $n$ = 400. Is the small p-value for $n$ = 400 indicative of a difference that has practical significance? Would you have been satisfied with just a report of the p-value? Comment briefly.

Quizplus · Accepted Answer

The Answer of To decide whether two different types of steel have the same true average fracture toughness values, $n$ specimens of each type are tested, yielding the following results: $$\begin{array} { c c c } 
\hline \text { Type } & \text { Sample Average } & \text { Sample St. Dev. } \
\hline 1 & 60.2 & 1.0 \
2 & 60.0 & 1.0 \
\hline
\end{array}$$ Calculate the $P$ -value for the appropriate two-sample $z$ test, assuming that the data was based on $n$ = 100. Then repeat the calculation for $n$ = 400. Is the small p-value for $n$ = 400 indicative of a difference that has practical significance? Would you have been satisfied with just a report of the p-value? Comment briefly.

To Decide Whether Two Different Types of Steel Have the Same