The ScamMore Energy Company is attempting to predict natural gas consumption for the month of January. A random sample of 50 homes was used to fit a regression of gas usage (in CCF) using as predictors Temperature = the thermostat setting (degrees Fahrenheit) and Occupants = the number of household occupants. They obtained the following results: $$\begin{array} { l c c }
\text { Variable } & \text { Coefficient } & \text { Std Err } \
\text { Intercept } & 21.684 & 4.122 \
\text { Temperature } & 0.9142 & 0.2918 \
\text { Occupants } & 2.244 & 1.315
\end{array}$$ In testing each coefficient for a significant difference from zero (two-tailed test at ? = .10), which is the most reasonable conclusion about the predictors?
A)Temperature is highly significant; Occupants is barely significant.
B)Temperature is not significant; Occupants is significant.
C)Temperature is less significant than Occupants.
D)Temperature is significant; Occupants is not significant.

Question

The ScamMore Energy Company is attempting to predict natural gas consumption for the month of January. A random sample of 50 homes was used to fit a regression of gas usage (in CCF) using as predictors Temperature = the thermostat setting (degrees Fahrenheit) and Occupants = the number of household occupants. They obtained the following results: $$\begin{array} { l c c } 
\text { Variable } & \text { Coefficient } & \text { Std Err } \
\text { Intercept } & 21.684 & 4.122 \
\text { Temperature } & 0.9142 & 0.2918 \
\text { Occupants } & 2.244 & 1.315
\end{array}$$ In testing each coefficient for a significant difference from zero (two-tailed test at ? = .10), which is the most reasonable conclusion about the predictors?
A)Temperature is highly significant; Occupants is barely significant.
B)Temperature is not significant; Occupants is significant.
C)Temperature is less significant than Occupants.
D)Temperature is significant; Occupants is not significant.

Quizplus · Accepted Answer

To determine whether the predictors are significant, we need to perform a t-test for each coefficient. The null hypothesis is that the coefficient is equal to zero, and the alternative hypothesis is that it is not equal to zero. We use α = 0.10, which corresponds to a two-tailed test with critical values ±1.645 for a sample size of 50 and a 10% level of significance.
The t-statistic for Temperature is (0.9142-0) / 0.2918 = 3.1274, which is greater than 1.645, so we reject the null hypothesis and conclude that Temperature is significant.
The t-statistic for Occupants is (2.244-0) / 1.315 = 1.7061, which is greater than 1.645, so we reject the null hypothesis and conclude that Occupants is significant.
Therefore, the most reasonable conclusion is that Temperature is highly significant, and Occupants is also significant, but to a lesser extent than Temperature. So, the best choice is (A).

The ScamMore Energy Company Is Attempting to Predict Natural Gas