As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types ofsteel. Use the following regression results to find the 95% confidence interval for the
Slope of the regression equation. $$\begin{array} { l r r r r }
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 7.671 & 1.507 & 5.09 & 0.000 \
\text { Carbon Content } & - 3.296 & 1.097 & - 3.01 & 0.010
\end{array}$$
A) -5.456 to -1.136
B) -4.393 to -2.199
C) 6.164 to 9.178
D) -5.666 to -0.926
E) 2.581 to 12.761

Question

As the carbon content in steel increases, its ductility tends to decrease. A researcher at a steel company measures carbon content and ductility for a sample of 15 types ofsteel. Use the following regression results to find the 95% confidence interval for the
Slope of the regression equation. $$\begin{array} { l r r r r } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 7.671 & 1.507 & 5.09 & 0.000 \
\text { Carbon Content } & - 3.296 & 1.097 & - 3.01 & 0.010
\end{array}$$
A) -5.456 to -1.136
B) -4.393 to -2.199
C) 6.164 to 9.178
D) -5.666 to -0.926
E) 2.581 to 12.761

Quizplus · Accepted Answer

We use the formula:
Confidence interval for slope = (slope estimate ± t* SE)

t* for a 95% confidence interval with 13 degrees of freedom (n-2) is 2.160.

Plugging in the values, we get:

Confidence interval for slope = (-3.296 ± 2.160*1.097)

Confidence interval for slope = (-3.296 ± 2.366)

Confidence interval for slope = (-5.666, -0.926)

Therefore, the 95% confidence interval for the slope of the regression equation is -5.666 to -0.926.

The answer is D, and it is the only choice that includes this range of values.

As the Carbon Content in Steel Increases, Its Ductility Tends