Tensile Strength Tests Were Carried Out on Two Different Grades

question 52

Essay

Tensile strength tests were carried out on two different grades of wire rod resulting in the accompanying data: $\begin{array}{llll}\hline \text { Grade } & \text { Sample Size } &\text { Sample Mean } & \text { Sample St. Dev. }\\ &&\left(\mathrm{kg} / \mathrm{mm}^{2}\right)\\\hline \text { AISI } & m= & \bar{x}= & s_{1}= \\1064 & 130 & 108 & 1.3 \\\text { AISI }& n= & \bar{y}= & s_{2}= \\1078 & 130 & 124 & 2.0 \\\hline \end{array}$

a. Does the data provide compelling evidence for concluding that "true" average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 $\mathrm { kg } / \mathrm { mm } ^ { 2 }$
? Test the appropriate hypotheses using the $P$
-value approach.
b. Estimate the difference between true average strengths for the two grades in a way that provides information about precision and reliability.

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Definitions:

Laboratory

A room or building equipped for scientific experiments, research, or teaching, or for the manufacture of drugs or chemicals.

Demand Characteristics

Aspects of a study that reveal the hypothesis or what is expected of participants, potentially influencing their behavior.

Double-Blind Procedure

An experimental methodology in which neither the participants nor the experimenters know who is receiving a particular treatment, to minimize bias.

Mode

The value that appears most frequently in a data set, a measure of central tendency.