Tensile Strength Tests Were Carried Out on Two Different Grades

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.