Casting aluminum Do the data provide convincing evidence at the a = 0.05 level of a

Chapter 12, Problem R12.2

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Exercises R12.1 to R12.3 refer to the following setting. In the casting of metal parts, molten metal flows through a “gate” into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined a random sample of 12 pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process. A scatterplot of the data is shown below.

A least-squares regression analysis was performed on the data. Some computer output and a residual plot are shown below. A Normal probability plot of the residuals (not shown) is roughly linear.

        

Casting aluminum Do the data provide convincing evidence at the \(\alpha=0.05\) level of a linear relationship between thickness and gate velocity in the population of pistons formed from this alloy of metal?