As the carbon content in steel increases its ductility tends

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

Predictor         Coef SE Coef      T      P

Constant         7.671    1.507   5.09 0.000

Carbon Content -3.296    1.097 -3.01 0.010

S = 2.36317   R-Sq = 41.0%   R-Sq(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

Solution

For df = n - 2 = 13, the critical t for a 95% confidence interval is

tcrit = 2.160368656

Now,

upper bound = B1 + t*sB1 = -3.296 - 2.160368656*1.097 = -5.665924416

upper bound = B1 + t*sB1 = -3.296 + 2.160368656*1.097 = -0.926075584

Thus, it is -5.665924416 to -0.926075584 [OPTION D]