Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
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Chapter 27, Problem 17E

a)

To determine

To perform the hypothesis test.

a)

Expert Solution
Check Mark

Answer to Problem 17E

There is sufficient evidence that the slope is non zero and there is association between weight of a car and its gas mileage.

Explanation of Solution

Given:

  Stats: Modeling the World Nasta Edition Grades 9-12, Chapter 27, Problem 17E , additional homework tip  1

Formula:

Test statistic:

  t=bβ0SEb

The null and alternative hypotheses:

  H0:β1=0Ha:β10

Test statistic:

  t=8.2136200.6738=12.190

The degrees of freedom = df = 48

Therefore, p-value would be,

P-value = 0 …Using excel formula, =TDIST(12.190,48,2)

Decision: P-value < 0.05, reject H0.

Conclusion: There is sufficient evidence that the slope is non zero and there is association between weight of a car and its gas mileage.

b)

To determine

To check the assumptions for regression.

b)

Expert Solution
Check Mark

Explanation of Solution

Given:

  Stats: Modeling the World Nasta Edition Grades 9-12, Chapter 27, Problem 17E , additional homework tip  2

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, because the 50 car models are less than 10% of the population.

Randomization condition: Satisfied, assuming car models were randomly selected.

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 histogram of the residual is roughly symmetric and unimodal.

c)

To determine

To state the hypothesis and conclusion.

c)

Expert Solution
Check Mark

Answer to Problem 17E

There is sufficient evidence that the slope is non zero and there is association between weight of a car and its gas mileage.

Explanation of Solution

Given:

  Stats: Modeling the World Nasta Edition Grades 9-12, Chapter 27, Problem 17E , additional homework tip  3

The null and alternative hypotheses:

  H0:β1=0Ha:β10

That means,

  H0: There is no association between weight of a car and its gas mileage.

  Ha: There is association between weight of a car and its gas mileage.

Conclusion: There is sufficient evidence that the slope is non zero and there is association between weight of a car and its gas mileage.

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