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

d. -5.666 to -0.926

Step-by-step explanation:

Here a pivotal quantity is where is the true slope of the regression  equation (unknown), is its least square estimate and is its estimated standard error. And T has t-distribution with n-2=15-2=13 degrees of freedom (n is the sample size). We have that , and because we want the 95% confidence interval, we should use the 2.5th quantile of the t distribution with 13 df, this value is -2.16 and the 95% confidence intervale is given by , i.e., . Therefore, the 95% confidence interval explicitly is (-5.666, -0.926)

75%

step-by-step explanation:

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.