Instruction 14-5
a Contractor Developed a Multiplicative Time-Series Model to Forecast

Instruction 14-5
A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the three-year period from 2008 to 2010. The following is the resulting regression equation:
$$\log _ { 10 } \hat { Y } = 3.37 + 0.117 X - 0.083 Q _ { 1 } + 1.28 Q _ { 2 } + 0.617 Q _ { 3 }$$
Where
$\hat { Y }$ is the estimated number of contracts in a quarter.
$X$ is the coded quarterly value with $X = 0$ in the first quarter of 2008 .
$Q _ { 1 }$ is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise.
$Q _ { 2 }$ is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise.
$Q _ { 3 }$ is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise.
-Referring to Instruction 14-5,in testing the coefficient for Q₁ in the regression equation (-0.083) ,the results were a t-statistic of-0.66 and an associated p-value of 0.530.Which of the following is the best interpretation of this result?

A) The number of contracts in the first quarter of the year is not significantly different than the number of contracts in an average quarter ( $\alpha$ = 0.05) .
B) The number of contracts in the first quarter of the year is not significantly different than the number of contracts in the fourth quarter for a given coded quarterly value of X ( $\alpha$ = 0.05) .
C) The number of contracts in the first quarter of the year is significantly different than the number of contracts in the fourth quarter for a given coded quarterly value of X ( $\alpha$ = 0.05) .
D) The number of contracts in the first quarter of the year is significantly different than the number of contracts in an average quarter ( $\alpha$ = 0.05) .