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 and
Summary statistics are given below.Find a 99% confidence interval for the mean lawn
Quality of all lawns sown with a seed density of 2.5. $\begin{array} { l l l l } \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } \\ \text { Seed Density } & 8 & 2.75 & 0.49099 \\ \text { Lawn Quality } & 8 & 45.625 & 3.712611 \end{array}$
Dependent variable is: Lawn Quality
$R$ squared $= 36.0\%$
$s = 9.073602$ 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) $( 31.1,53.9 )$
B) $( 30.4,54.6 )$
C) $( 42.0,47.0 )$
D) $( 6.7,78.2 )$