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.A 99% confidence interval for the mean lawn quality of all lawns sown with a seed density of 2.9 was found to be (32.3,56.3).Give an interpretation of this interval. $$\begin{array} { l c l l c }
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Seed Density } & 8 & 2.75 & 0.49099 & 4 \
\text { Lawn Quality } & 8 & 45.625 & 3.712611 & 35
\end{array}$$ Dependent variable is: Lawn Quality R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom $$\begin{array} { l l l l l }
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 33.14815 & 7.510757 & 4.413423 & 0.004503 \
\text { Seed Density } & 4.537037 & 2.469522 & 1.837213 & 0.115825
\end{array}$$
A)Based on this regression,we are 99% confident that the average lawn quality for lawns with a seed density of 2.9 pounds per 500 square feet is between 32.3 and 56.3.
B)Based on this regression,99% of all random samples will have an average lawn quality between 32.3 and 56.3.
C)Based on this regression,we are 99% confident that the average seed density will increase between 32.3 and 56.3 pounds per 500 square feet for each additional one-point increase in lawn quality.
D)Based on this regression,we are 99% confident that the average lawn quality will increase between 32.3 and 56.3 points for each additional pound of seed per 500 square feet.
E)Based on this regression,we are 99% confident that the lawn quality for a lawn with a seed density of 2.9 is between 32.3 and 56.3.

Question

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.A 99% confidence interval for the mean lawn quality of all lawns sown with a seed density of 2.9 was found to be (32.3,56.3).Give an interpretation of this interval. $$\begin{array} { l c l l c } 
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \
\text { Seed Density } & 8 & 2.75 & 0.49099 & 4 \
\text { Lawn Quality } & 8 & 45.625 & 3.712611 & 35
\end{array}$$ Dependent variable is: Lawn Quality R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom $$\begin{array} { l l l l l } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 33.14815 & 7.510757 & 4.413423 & 0.004503 \
\text { Seed Density } & 4.537037 & 2.469522 & 1.837213 & 0.115825
\end{array}$$
A)Based on this regression,we are 99% confident that the average lawn quality for lawns with a seed density of 2.9 pounds per 500 square feet is between 32.3 and 56.3.
B)Based on this regression,99% of all random samples will have an average lawn quality between 32.3 and 56.3.
C)Based on this regression,we are 99% confident that the average seed density will increase between 32.3 and 56.3 pounds per 500 square feet for each additional one-point increase in lawn quality.
D)Based on this regression,we are 99% confident that the average lawn quality will increase between 32.3 and 56.3 points for each additional pound of seed per 500 square feet.
E)Based on this regression,we are 99% confident that the lawn quality for a lawn with a seed density of 2.9 is between 32.3 and 56.3.

Quizplus · Accepted Answer

The 99% confidence interval for the mean lawn quality of all lawns sown with a seed density of 2.9 pounds per 500 square feet is given as (32.3,56.3). This means that if we were to take multiple samples and calculate their average lawn quality, 99% of the time the true mean lawn quality would fall between 32.3 and 56.3.

A Grass Seed Company Conducts a Study to Determine the Relationship