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 99% confidence interval for the mean lawn quality of all lawns sown with a seed
Density of 3.5 was found to be (33.3, 60.8) .Give an interpretation of this interval. Dependent variable is: Lawn quality
$R$ squared $= 36.08$
$s = 9.073602$ 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) Based on this regression, $99 \%$ of all random samples will have an average lawn quality between $33.3$ and $60.8$ .
B) Based on this regression, we are $99 \%$ confident that the average lawn quality will increase between $33.3$ and $60.8$ points for each additional pound of seed per 500 square feet.
C) Based on this regression, we are $99 \%$ confident that the lawn quality for a lawn with a seed density of $3.5$ is between $33.3$ and $60.8$ .
D) Based on this regression, we are $99 \%$ confident that the average seed density will increase between $33.3$ and $60.8$ pounds per 500 square feet for each additional one-point increase in lawn quality.
E) Based on this regression, we are $99 \%$ confident that the average lawn quality for lawns with a seed density of $3.5$ pounds per 500 square feet is between $33.3$ and $60.8$ .