Is there a positive relationship between sales of leaded gasoline and lead burden in the bodies of newborn infants? Researchers (Rabinowitz, et al, 1984) who were interested in answering this research question compiled data (leadcord.txt) on the monthly gasoline lead sales (in metric tons) in Massachusetts and mean lead concentrations (µl/dl) in umbilical-cord blood of babies born at a major Boston hospital over 14 months in 1980-1981.

Analyzing their data, the researchers obtained the following fitted line plot:

and standard regression analysis output:

The P-value for testing H₀ : β₁ = 0 against the alternative hypothesis H_A : β₁ ≠ 0 is 0.008. Therefore, since the test statistic is positive, the P-value for testing H₀ : β₁ = 0 against the alternative hypothesis H_A : β₁ > 0 is 0.008 ÷ 2 = 0.004. The P-value is less than 0.05. There is sufficient statistical evidence, at the 0.05 level, to conclude that β₁ > 0.

Furthermore, since the 95% t-multiplier is t(0.025, 12) = 2.1788, a 95% confidence interval for β₁ is:

0.014885 ± 2.1788(0.004719) or (0.0046, 0.0252).

The researchers can be 95% confident that the mean lead concentrations in umbilical-cord blood of Massachusetts babies increases between 0.0046 and 0.0252 µl/dl for every one-metric ton increase in monthly gasoline lead sales in Massachusetts. It is up to the researchers to debate whether or not this is a meaningful increase.