The Concessions Manager at a Beachside Park Recorded the High

question 111

Essay

The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive saturdays. The data are shown below. $$\begin{array} { c c c } \hline \text { Bottles Sold } & \text { Temperature } \left( { } ^ { \circ } \mathrm { F } \right) & \text { People } \\\hline 341 & 73 & 1625 \\425 & 79 & 2100 \\457 & 80 & 2125 \\485 & 80 & 2800 \\469 & 81 & 2550 \\395 & 82 & 1975 \\511 & 83 & 2675 \\549 & 83 & 2800 \\543 & 85 & 2850 \\537 & 88 & 2775 \\621 & 89 & 2800 \\897 & 91 & 3100 \\\hline\end{array}$$ a. Fit the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ to the data, letting $y$ represent the number of bottles of water sold, $x _ { 1 }$ the temperature, and $x _ { 2 }$ the number of people at the park.
b. Find the $95 \%$ confidence interval for the mean number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.
c. Find the $95 \%$ prediction interval for the number of bottles of water sold when the temperature is $84 ^ { \circ } \mathrm { F }$ and there are 2700 people at the park.

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Definitions:

Sold Separately

Items or services not included with the primary product and must be purchased independently.

Infringement Suit

A legal case brought against an individual or company for violating a patent, copyright, trademark, or other intellectual property rights.

Legal Expenses

Costs incurred by a business for legal services, such as attorney fees and court costs.

Goodwill

An intangible asset that arises when a business is acquired for more than the fair value of its net identifiable assets, representing the company's reputation, brand, or similar factors.