A Grass Seed Company Conducts a Study to Determine the Relationship

question 2

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 is given
Below.A 99% confidence interval for the mean lawn quality of all lawns sown with a seed
Density of 3.5 was found to be (33.3, 60.8) .Give an interpretation of this interval. Dependent variable is: Lawn quality
$R$ squared $= 36.08$
$s = 9.073602$ 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, \(99 \%\) of all random samples will have an average lawn quality between \(33.3\) and \(60.8\).
• B) Based on this regression, we are \(99 \%\) confident that the average lawn quality will increase between \(33.3\) and \(60.8\) points for each additional pound of seed per 500 square feet.
• C) Based on this regression, we are \(99 \%\) confident that the lawn quality for a lawn with a seed density of \(3.5\) is between \(33.3\) and \(60.8\).
• D) Based on this regression, we are \(99 \%\) confident that the average seed density will increase between \(33.3\) and \(60.8\) pounds per 500 square feet for each additional one-point increase in lawn quality.
• E) Based on this regression, we are \(99 \%\) confident that the average lawn quality for lawns with a seed density of \(3.5\) pounds per 500 square feet is between \(33.3\) and \(60.8\).

Understand the impact of the service rate and arrival rate on system utilization and queue lengths.

Describe the concepts of FIFO, LIFO, and other queue disciplines.

Apply Little's Law in appropriate contexts.

Understand the distinction between single-phase and multi-phase queuing systems.

---

Definitions:

Mean

The arithmetic average of a set of numbers, calculated by summing all the numbers and then dividing by the count of the numbers.

Mean

The arithmetic average of a set of numbers, calculated by dividing the sum of the values by the number of values.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Standard Deviations

A measure of the amount of variation or dispersion of a set of values from the mean.