The yield strength of CP titanium welds was measured for welds cooled at rates of \(10^{\circ}C/s,15^{\circ}C/s\ \text{and}\ 28^{\circ}C/s\). The results are presented in the following table. (Based on the article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds,” D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s.)
\(\begin{array}{}
\hline
\text{Cooling Rate}&\text{Yield Strenghts}\\
\hline
10&71.00&75.00&79.67&81.00&75.50&72.50&73.50&78.50\\
15&63.00&68.00&73.00&76.00&79.67&81.00\\
28&68.65&73.70&78.40&84.40&91.20&87.15&77.20&80.70&84.85&88\\
\hline
\end{array}\)
a. Construct an ANOVA table. You may give a range for the P-value. b. Can you conclude that the yield strength of CP titanium welds varies with the cooling rate?
The following advanced exercise use a generalized ratio test to determine convergence of some series that arise in particular applications, including the ratio and root test, are not powerful enough to determine their convergence. The test states that if $
The following definition is discussed in advanced mathematics courses.
Evaluate