Questions: Determine whether the association between the two variables is positive or negative. The weight of a car (in pounds) and its fuel efficiency (in miles per gallon)

Determine whether the association between the two variables is positive or negative.
The weight of a car (in pounds) and its fuel efficiency (in miles per gallon)

Transcript text: Determine whether the association between the two variables is positive or negative. The weight of a car (in pounds) and its fuel efficiency (in miles per gallon)

Solution

Solution Steps

Step 1: Collect Data

Data has been collected with weights of cars (in pounds) and their fuel efficiency (in miles per gallon).

Step 2: Plot Data

A scatter plot is created with car weight on the x-axis and fuel efficiency on the y-axis to visually inspect the relationship.

Step 3: Calculate Correlation Coefficient (r)

The Pearson correlation coefficient (r) is calculated using the formula for Pearson's r. The calculated value of r is -0.99.

Step 4: Interpret the Correlation

Since r = -0.99 < 0, there is a negative association between the weight of a car and its fuel efficiency, which aligns with common expectations.

Step 5: Statistical Significance

The p-value of the correlation coefficient is 0. If the p-value is less than 0.05, the correlation is considered statistically significant, indicating that the observed association is not due to random chance.