Question

jessica investigates the relationship between caffeine intake and performance on a class test for high school students. before her sample of students takes an exam, she notes the number of cups of coffee they consumed two hours before the test. she obtains their scores after the test is over. she then calculates the correlation coefficient between the two variables and finds it to be +0.82. which of the following conclusions should jessica draw from this value?

○ caffeine consumption has no association with performance on a test.

○ higher caffeine consumption is related to higher exam scores.

○ caffeine consumption causes higher scores.

○ eighty - two percent of the students consumed caffeine prior to the exam.

Explanation:

1. Analyze the correlation coefficient: A positive correlation coefficient (here, +0.82) indicates a positive linear relationship between two variables.

• The first option is wrong because a non - zero correlation coefficient (0.82 is far from 0) shows there is an association.
• The second option: Since the correlation coefficient is positive and moderately strong (close to 1), it implies that as one variable (caffeine consumption) increases, the other (exam scores) tends to increase. So higher caffeine consumption is related to higher exam scores.
• The third option is wrong because correlation does not imply causation. Just because two variables are correlated does not mean one causes the other.
• The fourth option is wrong because the correlation coefficient does not represent the percentage of students who consumed caffeine. It measures the strength and direction of the linear relationship between two variables.

Answer:

B. Higher caffeine consumption is related to higher exam scores.