An engineer at an aluminum castings plant assesses the relationship between the hydrogen content and the porosity of aluminum alloy castings. The engineer collects a random sample of 14 castings and measures the following properties of each casting: hydrogen content, porosity, and strength.

The engineer uses the Pearson correlation to examine the strength and direction of the linear relationship between each pair of variables.

The Pearson correlation coefficient between hydrogen content and porosity is 0.625 and represents a positive relationship between the variables. As hydrogen increases, porosity also increases. The p-value is 0.017, which is less than the significance level of 0.05. The p-value indicates that the correlation is significant.

The Pearson correlation coefficient between hydrogen content and strength is −0.790 and the p-value is 0.001. The p-value is less than the significance level of 0.05, which indicates that the correlation is significant. As hydrogen content increases, strength tends to decrease. The Pearson correlation coefficient between porosity and strength is −0.527 and the p-value is 0.053. The p-value is close to the significance level of 0.05, which provides inconclusive evidence for the association between porosity and strength. Because the sample has only 14 observations, the engineer decides to collect more data to better understand the association between the variables.

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