To Decide Whether Two Different Types of Steel Have the Same

question 11

Essay

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.

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Definitions:

Social Loafing

The circumstances in which persons engaged in a group task demonstrate lower efforts in goal accomplishment than in solitary work conditions.

Personal Accountability

The responsibility of individuals for their actions and decisions, acknowledging their consequences.

Group Situation

A scenario in which multiple individuals are present, interacting, and possibly working towards a common goal or within a common context.

Personal Control

The belief that one has the ability to influence or control the events in their life, contributing to psychological empowerment.