Question

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of $25$students was selected from a large high school. For each student, $x=footlength\&y=height$were recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following is a $95\%$confidence interval for the population slope ${\beta }_1$?

a.$3.0867\pm 0.4117$

b. $3.0867\pm 0.8518$

c.$3.0867\pm 0.8069$

d.$3.0867\pm 0.8497$

e.localid="1654193042763" $3.0867\pm 0.8481$

Short answer

The correct option is option (b)

$3.0867\pm 0.8518$

Step-by-step solution

Given Information

Given in the question that

$n=25$

$c=0.95$

we have to determine the correct option.

Explanation

The confidence interval is computed as

$b\pm t*\times S{E}_b$

where $b_1=3.0867$and $S{E}_{b1}=0.4117$which is given in the computer output.

The degree of difference is

$$\begin{gathered} df=n-2 \\ =25-2 \\ =23 \end{gathered}$$

The critical T value can be found in the $T$distribution table, so $t*is2.069$.

Therefore, the confidence interval is

localid="1654497378353" $$\begin{gathered} b\pm t*S{E}_b=3.0867\pm 2.069\times 0.4117 \\ =3.0867\pm 0.8518 \end{gathered}$$