Chapter 27, Problem 5E

a)

To determine

To check the assumptions and conditions for inference.

Explanation of Solution

Given:

  

  

The conditions are: straight enough, Independence, Randomization, Random residual, Does plot thicken? and Nearly normal condition.

We will check it one by one.

Straight enough condition: Satisfied, because no curvature is present in the scatterplot.

Independence assumption: Satisfied, assuming that the movies are independent.

Randomization condition: Satisfied, assuming that the sample is representative for the population.

Random residuals condition: Satisfied, because there is no obvious pattern in the residual plot.

Does the plot thicken? condition: Satisfied, because the vertical spread in the residual plot is not increasing or decreasing.

Nearly normal condition: Satisfied, because the normal quantile plot of the residual is roughly linear.

c)

To determine

To find the 95% confidence interval for slope.

Answer to Problem 5E

The 95% confidence interval for slope is,

  $(0.4146,1.0142)$

Explanation of Solution

Given:

  

  

Formula:

Confidence interval for slope is,

  $(b-t_c\times S{E}_b,b+t_c\times S{E}_b)$

First, need to find critical value $t_c$ .

Critical value for df = 118 and confidence level = 0.95 is,

  $t_c=1.98$ …Using excel formula, =TINV(0.05,118)

Therefore, the 95% confidence interval for slope is,

  $\begin{array}{l}(0.714400-1.98\times 0.1514,0.714400+1.98\times 0.1514)\\ (0.4146,1.0142)\end{array}$