The Concessions Manager at a Beachside Park Recorded the High $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$

question 69

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.


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:

Manufacturing Overhead

All indirect costs associated with manufacturing, excluding direct materials and direct labor, such as utilities, depreciation, and maintenance of factory equipment.

Predetermined Overhead Rate

An estimated rate used to allocate manufacturing overhead costs to products or services.

Manufacturing Cost

All expenses directly related to the production of goods, including raw materials, labor, and factory overhead.

Machine-Hours

A measure of production time, indicating the total hours that machines are operating in the manufacturing process.