Question

A $95\%$confidence interval for the population slope $\beta$is

(a) $1.0466\pm 149.5706$.

(b) $1.0466\pm 0.2415$.

(c) $1.0466\pm 0.2387$.

(d) $1.0466\pm 0.1983$.

(e) $1.0466\pm 0.1126$.

Short answer

The slope of the true regression line is $1.0466\pm 0.2415$. Therefore, option (b) is the correct option.

Step-by-step solution

Given Information

Given in the question that,

$n=16$

$b=-1.0466$

${\mathrm{SE}}_b=0.1126$

Explanation

The degrees of freedom is the sample size decreased by 2 :

$df=n-2$

$=16-2$

$=14$

The critical $t$-value can be found in table $\mathrm{B}$in the row of $df=14$and in the column of $c=95\%$as:

$t^{*}=2.145$

Thus, the confidence interval is as:

$b\pm t^{*}\times {\mathrm{SE}}_b$$=1.0466\pm 2.145\times 0.1126$

$=1.0466\pm 0.2415$