Create a Confidence Interval for the Slope of a Regression $= 7.67 - 3.30$

question 15

Multiple Choice

Create a confidence interval for the slope of a regression equation.
-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 of steel.
Based on these data he obtained the following regression results. The regression equation is
Ductility $= 7.67 - 3.30$ Carbon Content

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 7.671 & 1.507 & 5.09 & 0.000 \\ \text { Carbon Content } & - 3.296 & 1.097 & - 3.01 & 0.010 \end{array}$
$$S = 2.36317 \quad \mathrm { R } - \mathrm { Sq } = 41.0 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 36.5 \%$$
The 95% confidence interval for the slope of the regression equation is

• 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

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Definitions:

Sample Mean

The arithmetic average of a set of sample values, used as an estimate of the population mean.

Null Hypothesis

A statement or assumption that there is no significant difference or effect, serving as the default conclusion until evidence suggests otherwise.

Critical Value

A threshold in statistical hypothesis testing that defines the boundary or limit beyond which an observed test statistic is considered statistically significant.

Perfect Adjustment

An ideal state in statistical models where the predicted values and actual values align perfectly, indicating no prediction error.