Chapter 7, Problem 40E

(a)

To determine

To make a scatterplot for these data.

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. To see if the device is accurate they conducted the calibration test. Now, the table of weight in motion and static weight is given in the table in the question. The scatterplot of the weight-in-motion and the static weight is as:

  

The weight-in-motion is on the horizontal axis and the static weight is on the vertical axis.

(b)

To determine

To describe the direction, form and strength of the plot.

Answer to Problem 40E

There is a positive, moderately linear relationship between the weight-in-motion and static weight.

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. To see if the device is accurate they conducted the calibration test. From the scatterplot in part (a), we can see that the relationship is positive and linear. However, the correlation is only moderately strong because the points do not form a great line. Thus, there is a positive, moderately linear relationship between the weight-in-motion and static weight.

(c)

To determine

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

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. To see if the device is accurate they conducted the calibration test.The relationship between the weight-in-motion and static weight is positive and linear as seen by the scatterplot. However, the correlation is only moderately strong because the points do not form a great line. Therefore, we can say that the static weight of the cars are almost consistently lower than the weight of cars in motion.

(d)

To determine

To calculate the correlation.

Answer to Problem 40E

The correlation between the weight-in-motion and static weight is $0.965$ .

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. To see if the device is accurate they conducted the calibration test. The table is as follows:

Weight-in-Motion	Static Weight
26	27.9
29.9	29.1
39.5	38
25.1	27
31.6	30.3
36.2	34.5
25.1	27.8
31	29.6
35.6	33.1
40.2	35.5

Now, for calculating the correlation between the weight-in-motion and the static weight we will be using excel. Thus, we have,

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,

  $=\text{CORREL}\left(\text{G8:G22,H8:H22}\right)$

And the answer to this will be as:

Correlation coefficient

0.965

So, the correlation between the weight-in-motion and static weightis $0.965$ .

(e)

To determine

To explain how would this change the correlation if the trucks were weighed in kilograms.

Answer to Problem 40E

There would be no change.

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. The correlation between the weight-in-motion and static weight is $0.965$ . Now, if the trucks were weighed in kilograms then, there would be no change in the correlation as the data would all change by the same amount, so there would be no change in correlation. And the units do not affect the correlation.

(f)

To determine

To explain do any points deviate from the overall pattern and what does the plot say about a possible recalibration of the weight in motion scale.

Explanation of Solution

The department of transportation hoped that they could measure the weights of big trucks without actual stopping the trucks by using a developed weight-in-motion scale. The correlation between the weight-in-motion and static weight is $0.965$ .The only major deviation is the fourth point, where the static weight was greater than the weight in motion. This generally shows that the recalibration should decrease the weights in motion.