Chapter PVII, Problem 2RE

(a)

To determine

To find: the number of different products were included these analyses.

Answer to Problem 2RE

59

Explanation of Solution

Given:

Degree of freedom = 57

Calculation:

Degrees of freedom is $n-2$ .

The degrees of freedom are 57. Thus, $n=59$ .

Therefore, there are 59 different products are in the analysis.

(b)

To determine

To find: the fraction of the variation in the retail price discussed by polishing time.

Explanation of Solution

Given:

  $R^2=84.5\%$

The polishing time therefore explains 84.5 percent of the variation in the retail price. 84.5% of the retail price difference is compensated for by this model.

(c)

To determine

To construct: the 95 percent confidence interval for this relationship's slope.

Answer to Problem 2RE

(2.208957, 2.775923)

Explanation of Solution

Given:

The t-distribution with $n-2$ degrees of freedom.

Formula used:

Confidence interval

  $b_1\pm t_{n-2}^{\ast }\times SE\left(b_1\right)$

Calculation:

Therefore, the critical value is $t_{57}^{\ast }=2.002$

So a 95% confidence interval for ${\beta }_1$ is

  $\begin{array}{c}{b}_1\pm t_{n-2}^{\ast }\times SE\left(b_1\right)\\ \Rightarrow 2.49244\pm 2.002\times 0.1416\\ \Rightarrow 2.49244\pm 0.283483\\ \Rightarrow \left(2.208957,2.775923\right)\end{array}$

(d)

To determine

To Explain: the interval.

Explanation of Solution

There are 95 percent confident that the retail price increases, on average, between 2.2089 and 2.7759 for every additional raise in polishing time.