Question

P-Values In Exercises 13–16, write a statement that interprets the P-value and includes a conclusion about linear correlation.

Using the data from Exercise 7 “Car Weight and Fuel Consumption,” the P-value is 0.000.

Short answer

The p-value equal to 0.000 indicates that there is almost zero probability of getting the computed linear correlation measure that extreme between highway fuel consumption and the weight of cars, assuming that there exists no linear correlation between the variables.

Thus, it can be concluded that there is sufficient evidence to infer that there exists a linear correlation between highway fuel consumption and the weight of cars.

Step-by-step solution

Given information

The p-value of linear correlation between highway fuel consumption and the weight of cars is equal to 0.000.

Interpret the p-value

The probability value that the computed value of r is due to chance, and there is no actual correlation between the two variables is determined by the p-value.

In this case, it implies the chance of getting the value as extreme as the computed correlation measure, which is almost zero, under the supposition that highway fuel consumption is not linearly correlated to the weight of the cars.

State the conclusion

The criteria to derive the conclusion include the following:

• When the p-value is less than or equal to 0.05, it indicates that there is significant evidence that a linear correlation exists between the two variables.

• When the p-value is greater than 0.05, it indicates that there is insufficient evidence that a linear correlation exists between the two variables.

The p-value for correlation between fuel consumption and weight is equal to 0.000.

The p-value is less than 0.05.

Therefore, it can be concluded that there exists a linear correlation between fuel consumption and the weight of the car.