A Grass Seed Company Conducts a Study to Determine the Relationship

question 8

Multiple Choice

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% prediction interval for the lawn quality of a lawn sown with a seed density of 2.9 was determined to be $$( 10.6,82.0 )$$ . $$\begin{array} { l c l l c } \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \\\text { Seed Density } & 8 & 2.75 & 0.49099 & 4 \\\text { Lawn Quality } & 8 & 45.625 & 3.712611 & 35\end{array}$$ 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 mean seed density will increase between 10.6 and 82.0 for each additional point of lawn quality over 2.9 pounds.
• B)Based on this regression,we are 99% confident that the mean lawn quality will increase between 10.6 and 82.0 for each additional pound of seed density over 2.9 pounds.
• C)Based on this regression,we are 99% confident that a lawn with a seed density of 2.9 pounds per 500 square feet will have a lawn quality between 10.6 and 82.0.
• D)Based on this regression,we are 99% confident that the mean lawn quality for lawns with a seed density of 2.9 pounds per 500 square feet will be between 10.6 and 82.0.
• E)Based on this regression,we know that 99% of all random samples will have a lawn quality between 10.6 and 82.0.

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Definitions:

Central Limit Theorem

A statistical principle stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Sampling Distribution

The likelihood distribution of a statistic derived from numerous samples taken from a particular population.

Considered Normal

A term often used in statistics and probability to refer to data or distribution patterns that fit within a normal (Gaussian) distribution, characterized by a symmetric bell-shaped curve.

Standard Error

A statistical measure that estimates the accuracy with which a sample distribution represents a population by using the standard deviation.