Suppose a random sample of 20020 -year-old men is selected from a population and their heights and weights are recorded. A regression of weight on height yields

\[ \begin{equation*} \widehat{\text { Weight }}=-99.41+3.94 \times \text { Height, } R^{2}=0.81, \text { SER }=10.2 \tag{2.15} \end{equation*} \]

where Weight is measured in pounds and Height is measured in inches. Two of your classmates differ in height by 1.5 inches. Construct a \(99 \%\) confidence interval for the difference in their weights.