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Chapter 14: Q. 14.65 (page 571)

In each of Exercises 14.64-14.69, apply Procedure 14.2 on page 567 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the predictor variable.
14.65 Corvette Prices. Refer to Exercise 14.59;90%

Short Answer

Expert verified

The Confidence interval at90% is [71.0382,85.8079].

Step by step solution

01

Given information

To determine 90%confidence interval that refer to Exercise 14.59.

02

Explanation

The provided sample data as follows:

x
12
24
10
9
15
17
9
18
16
22
y
84
79
81
90
81
85
82
84
83
75

Determine the degree of freedom as follows:
df=n-2

=10-2

=8
The value of t0.1is 1.860, as determined by the student t-test.

Determine the confidence interval as follows:

x¯-t0.1×sn=82.4-1.860×3.949710

=71.0382

x¯-t0.1×sn=82.4+1.860×3.949710

=85.8079

Finally,

Confidence interval=[71.0382,85.8079].

03

Explanation

Plot a graph as follows:

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Most popular questions from this chapter

Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks, useα=0.01presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

To find and interpret a confidence interval, at the specified confidence level 99%for the slope of the population regression line that relates the response variables to the predictor variable.

Body Fat. In the paper "Total Body Composition by Dual-Photon ( G153id) Absorptiometry" (American Journal of Clinical Nutrition, Vol.40,pp.834-839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry. Each adult's age and percentage of body fat are shown on the WeissStats site.

a. Decide whether you can reasonably apply the regression t-test. If so, then also do part (b).

b. Decide, at the 5%significance level, whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

In Exercises 14.12-14.21, we repeat the data and provide the sample regression equations for Exercises 4.48 -4.57.

a. Determine the standand error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

PCBs and Pelicans. Use the data points given on the WeissStats site for shell thickness and concentration of PCBs for 60 Anacapa pelican eggs referred to in Exercise 14.40.
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