The Accompanying 25 Observations on Fracture Toughness of Base Plate

question 19

Essay

The accompanying 25 observations on fracture toughness of base plate of 18% nickel maraging steel were obtained. Suppose a company will agree to purchase this steel for a particular application only if it can be strongly demonstrated from experimental evidence that "true" average toughness exceeds 80. Assuming that the fracture toughness distribution is symmetric, state and test the appropriate hypotheses level .05 and compute a P-value. $$\begin{array} { r r r r r r r r r } \hline 74.5 & 76.9 & 77.6 & 78.1 & 78.3 & 78.5 & 79.1 & 79.2 & 80.3 \\\hline 80.5 & 80.7 & 80.8 & 81.1 & 81.2 & 81.2 & 81.9 & 82.0 & 82.9 \\\hline 83.1 & 84.6 & 84.7 & 85.1 & 87.2 & 88.7 & 98.7 & & \\\hline\end{array}$$

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Definitions:

Pearson Correlation

A measure of the linear correlation between two variables X and Y, giving a value between -1 and 1 which indicates the extent of their linear relationship.

Coefficient

A numerical or constant factor in a mathematical equation that multiplies a variable.

Spearman Rank-Order

An approach that doesn't rely on parameters to gauge the correlation of ranks, examining the extent to which a monotonic function can accurately represent the linkage between two variables.

Nominal Level

The simplest level of measurement that classifies data into distinct categories within which no order or ranking can be inferred.