Operations Managers Often Use Work Sampling to Estimate How Much $\quad\quad y =$

question 114

Essay

Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling-which involves observing workers at random points in time-was applied to the staff of the catalog sales department of a clothing manufacturer.
The department applied regression to the following data collected for 40 consecutive working days:
TIME: $\quad\quad y =$ Time spent (in hours) taking telephone orders during the day
ORDERS: $\quad x _ { 1 } =$ Number of telephone orders received during the day
WEEK: $\quad\quad x _ { 2 } = 1$ weekday, 0 if Saturday or Sunday

Consider the complete 2nd-order model:
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } \left( x _ { 1 } \right) ^ { 2 } + \beta _ { 3 } x _ { 2 } + \beta _ { 4 } x _ { 1 } x _ { 2 } + \beta _ { 5 } \left( x _ { 1 } \right) ^ { 2 } x _ { 2 }$$ Explain how to conduct a test to determine if a quadratic relationship between total order time and the number of orders taken is necessary in the regression model above. Specify the null and alternative hypotheses that are to be tested.

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Definitions:

Strategic Planning

The process of defining a company's direction and making decisions on allocating its resources to pursue this strategy.

Environmental Data

Information that relates to the natural world and the impact of human activities on it, used in analysis and decision making.

Public Relations

The practice of managing and disseminating information from an individual or an organization to the public in order to influence their perception.

Stakeholder Management

The process of identifying, analyzing, and managing individuals or groups that have an interest or stake in an organization's actions and outcomes.