A statistician wanted to construct a $95\%$ confidence interval for the population slope between height (in inches) and weight (in pounds) of his co-workers. He made height the explanatory (independent) variable and weight the response (dependent) variable.
He selected a random sample of $30$ people from work and asked them to list their height and weight. After seeing his conditions were satisfied, he constructed the interval and got a result of $(1.97, 2.89)$.
Which of the following is the correct interpretation of the interval in the context of this study?