Question

which of the following is the best example of a positive correlation? multiple choice your chances of getting an a increase as the difficulty of the test decreases. the less interesting the lecture, the less likely you are to remember everything the instructor said. you should study longer because that helps you get a better grade. alicia loves to eat ice cream on hot afternoons.

Answer 1

The incorrect choice provided for a positive correlation is an actually negative correlation, exemplified by a decrease in exam grades with increased TV watching before exams. The Pearson's Correlation Coefficient measures the strength and direction of the relationship, with a value closer to 1 indicating a strong positive correlation.

Step-by-step explanation:

The best example of a positive correlation from the provided choices is, 'Which statement best illustrates a negative correlation between the number of hours spent watching TV the week before an exam and the grade on that exam?' This statement incorrectly indicates 'positive correlation' rather than negative correlation which is actually present: as the number of hours spent watching TV increases, the grade on the exam is likely to decrease, and vice versa. Nevertheless, to address the question accurately, a positive correlation occurs when both variables move in the same direction, meaning as one variable increases, the other variable also increases.

A real-world example of this would be the relationship between the size of a wildfire and the amount of smoke produced; larger wildfires tend to produce more smoke. The Pearson's Correlation Coefficient can quantitatively describe this relationship, with higher values (closer to 1) indicating stronger positive correlations.

It's also essential to understand that correlation does not imply causation. Just because two variables show a correlation doesn't mean that one causes the other, as may be mistakenly inferred in the ice cream sales and burglary rates example. This is an instance where both variables may increase due to a third variable, like warm weather, leading to both more ice cream consumption and more burglaries, but not causing one another.

Answer 2

The best example of a positive correlation is your chances of getting an A increase as the difficulty of the test decreases.

Step-by-step explanation:

A positive correlation means that as one variable increases, the other variable also increases. In the given options, the best example of a positive correlation is:

• Your chances of getting an A increase as the difficulty of the test decreases.

In this example, as the difficulty of the test decreases, the chances of getting an A increase. This demonstrates a positive correlation where both variables move in the same direction.