Asked by Elia Adele Marcheline on Apr 26, 2024
Verified
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. Variable Count Mean StdDev Range Seed Density 82.750.490994 Lawn Quality 845.6253.71261135\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} Variable Seed Density Lawn Quality Count 88 Mean 2.7545.625 StdDev 0.490993.712611 Range 435 Dependent variable is: Lawn Quality R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 33.148157.5107574.4134230.004503 Seed Density 4.5370372.4695221.8372130.115825\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} Variable Constant Seed Density Coefficient 33.148154.537037 SE(Coeff) 7.5107572.469522 t-ratio 4.4134231.837213 P-value 0.0045030.115825
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.
Seed Density
The number of seeds per unit area or volume, which can affect plant growth and crop yield.
Lawn Quality
A measure of the health, appearance, and overall condition of a grassy area or garden.
- Comprehend the process and analysis of confidence intervals for the slope in linear regression.
- Attain the skill to evaluate and interpret confidence and prediction intervals in the ambit of regression analysis.
Verified Answer
AB
Alexander BakerApr 27, 2024
Final Answer :
A
Explanation :
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.
Learning Objectives
- Comprehend the process and analysis of confidence intervals for the slope in linear regression.
- Attain the skill to evaluate and interpret confidence and prediction intervals in the ambit of regression analysis.
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