Chapter 12.1, Problem 27E

To determine

To find: the correct option of the following is a 95 percent confidence interval.

Answer to Problem 27E

  $3.0867\pm 0.8518$

Explanation of Solution

Given:

  

  $\begin{array}{l}n=25\\ c=95\%=0.95\end{array}$

Formula used:

Confidence intervals are

  $b\pm t^{\ast }\times S{E}_b$

Calculation:

The calculation of the slope $b_1$ is mention in the row “Foot length” and in the column “Coef” of the mention in the computer output:

  $b_1=3.0867$

The calculated standard deviation of the slope $S{E}_{b_1}$ is mention in the row “Foot length” and in the column “SE Coef” of the mention in the computer output:

  $S{E}_{b_1}=0.4117$

The critical t-value could be found in the T distribution table in the row of $df=n-2=25-2=23$ and in the column of $c=95\%$ :

  $t^{\ast }=2.069$

The boundaries of the confidence interval are

  $\begin{array}{c}b\pm t^{\ast }\times S{E}_b=3.0867\pm 2.069\times 0.4117\\ =3.0867\pm 0.8518073\\ =3.0867\pm 0.8518\end{array}$

Hence, the correct option is (b)