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 7, Problem 33E

(a)

To determine

To make a scatterplot for these data.

(a)

Expert Solution
Check Mark

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. The scatterplot for the same is given as follows:

  Stats: Modeling the World Nasta Edition Grades 9-12, Chapter 7, Problem 33E

The horsepower is on the horizontal axis and the highway gas mileage is on the vertical axis.

(b)

To determine

To describe direction, strength and form of the plot.

(b)

Expert Solution
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Answer to Problem 33E

Direction is negative, form is linear and the strength is moderately strong.

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. And the scatterplot of the horsepower and the highway gas mileage is in part (a). By this we know that the association between the horsepower and the highway gas mileage is negative, linear and moderately strong since the points form a downward linear trend and the points are neither too clustered nor too scattered.

(c)

To determine

To find the correlation between the horsepower and the miles per gallon.

(c)

Expert Solution
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Answer to Problem 33E

The correlation between the horsepower and the highway gas mileage is 0.869 .

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. Then we will calculate the correlation coefficient of horsepower and the highway gas mileage by using the excel. The data is as:

    Horsepower Highway gas mileage
    200 32
    230 30
    200 30
    148 32
    291 22
    300 20
    295 21
    140 40
    166 34
    138 36
    306 28
    300 18
    212 25
    158 34
    150 30

Formula used:

The CORREL function calculates the correlation coefficient between the two data sets in the excel. The syntax is as:

CORREL(array 1 ,array 2 )

Calculation:

Now, we will calculate the correlation coefficient using the excel. We will use the above CORREL function for this and we will have,

  =CORREL(G8:G22,H8:H22)

And the answer to this will be as:

    Correlation coefficient -0.868682726

So, the correlation between the horsepower and the highway gas mileage is 0.869 .

(d)

To determine

To write a few sentences telling what the plot says about fuel economy.

(d)

Expert Solution
Check Mark

Explanation of Solution

The information about the horsepower and the highway gas mileage is given in the question. And the correlation between the horsepower and the highway gas mileage is 0.869 . Now, since the scatterplot has points in a downward trend, it seems that the greater the horsepower the vehicle has, the less fuel efficient the vehicle is. Also if you want to your vehicle to be fuel efficient i.e., greater mileage, you should buy a vehicle with less horsepower.

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