A Grass Seed Company Conducts a Study to Determine the Relationship

A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn.Eight similar
Plots of land are selected and each is planted with a particular density of seed.One month
Later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given
Below.A 95% confidence interval for the slope of the regression line was determined to be (-1.51, 10.58) .Give an interpretation of this interval. Dependent variable is: Lawn Quality
$R$ squared $= 36.0$ 8
$s = 9.073602$ with $8 - 2 = 6$ degrees of freedom
$\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Constant } & 31.14815 & 7.510757 & 4.413423 & 0.004503 \\ \text { Seed Density } & 4.537037 & 2.469522 & 1.837213 & 0.115825 \end{array}$

A) We are $95 \%$ confident that each additional point on the lawn quality scale will increase the average seed density by $- 1.51$ to $10.58$ pounds per 500 square feet.
B) We are $95 \%$ confident that a randomly selected plot will have a lawn quality between $- 1.51$ and $10.58$ points.
C) Based on this regression, we are $95 \%$ confidence that the average lawn quality is between $- 1.51$ and $10.58$ points.
D) Based on this regression, each additional pound of seed per 500 square feet will increase the average lawn quality by $- 1.51$ to $10.58$ points, with $95 \%$ confidence.
E) We are $95 \%$ confident that the average lawn quality will increase between $- 1.51$ and $10.58$ points per year.

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