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

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: $\quad y =$ Time spent (in hours) taking telephone orders during the day
ORDERS: $\quad x _ { 1 } =$ Number of telephone orders received during the day
WEEK: $\quad x _ { 2 } = 1$ weekday, 0 if Saturday or Sunday
Consider the complete 2 nd-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.