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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?

A

$95\%$ of the time the population slope relating height to weight for the statistician's co-workers will be in the interval from $1.97$ to $2.89$.

B

The statistician is $95\%$ confident that for each additional increase in pounds, the average height will increase between $1.97$ to $2.89$ inches.

C

The statistician is $95\%$ confident that for each additional increase in pounds, the height will increase between $1.97$ to $2.89$ inches

D

The statistician is $95\%$ confident that the interval from $1.97$ to $2.89$ captures the sample slope for relating height to weight of his co-workers.

E

The statistician is $95\%$ confident that the interval from $1.97$ to $2.89$ captures the population slope for relating height to weight for his co-workers.

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