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% prediction interval for the lawn quality of a lawn sown with a seed density of 1.9 was determined to be (5.3, 78.3) .Give an interpretation of this interval. Dependent variable is: Lawn Quality
$R$ squared $= 36.0$ 웅
$s = 9.073602$ 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, we are $99 \%$ confident that the mean seed density will increase between $5.3$ and $78.3$ for each additional point of lawn quality over $1.9$ pounds.
B) Based on this regression, we are $99 \%$ confident that the mean lawn quality for lawns with a seed density of $1.9$ pounds per 500 square feet will be between $5.3$ and $78.3$ .
C) Based on this regression, we are $99 \%$ confident that the mean lawn quality will increase between $5.3$ and $78.3$ for each additional pound of seed density over $1.9$ pounds.
D) Based on this regression, we know that $99 \%$ of all random samples will have a lawn quality between $5.3$ and $78.3$ .
E) Based on this regression, we are $99 \%$ confident that a lawn with a seed density of $1.9$ pounds per 500 square feet will have a lawn quality between $5.3$ and $78.3$ .