Chapter 12.1, Problem 10E

(a)

To determine

To find: the critical value and confidence interval for a 90% confidence interval.

Answer to Problem 10E

Critical value: 1.761

Confidence interval: (0.004243984, 0.012894016)

Explanation of Solution

Given:

  

Formula used:

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{*}\times S{E}_{b_1}\\ b+t^{*}\times S{E}_{b_1}\end{array}$

Calculation:

Slope $b_1$ is mention in the row “Perch” and in the column “Coefficient” of the mention output from computer

  $b_1$ =0.008569

The calculated standard deviation of the slope $S{E}_{b_1}$ is mention in the row “Perch” and in the column “stdev.” of the mention output from the computer

  $S{E}_{b_1}$ =0.002456

Degree of freedom = 16-2=14

The t-value can be determine in the student’s T distribution table df=14 and column of c= 90%

  $t^{*}=1.761$

The boundaries of the confidence interval

  $\begin{array}{l}b-t^{*}\times S{E}_{b_1}=0.008569-1.761\times 0.002456=0.004243984\\ b+t^{*}\times S{E}_{b_1}=0.008569+1.761\times 0.002456=0.012894016\end{array}$

(b)

To determine

To Explain: the interval from part (a).

Explanation of Solution

Given:

  

Calculation:

From part (a)

  $\begin{array}{l}b-t^{*}\times S{E}_{b_1}=0.008569-1.761\times 0.002456=0.004243984\\ b+t^{*}\times S{E}_{b_1}=0.008569+1.761\times 0.002456=0.012894016\end{array}$

There are 90 percent confident that the true slope of the regression line of the population is between 0.004243984 and 0.012894016.

(c)

To determine

To Explain: the meaning of 90% confident.

Explanation of Solution

Given:

  

The 90 percent confidence interval shows the slope of the true regression line. It is also say that 90 percent confidence means that it is predicted about 90 percent of all samples to have a 90 percent confidence interval that is having the true population parameter.