Correlation Coefficients: Interpret and Calculate Effectively

A study shows that the number of hours students study and their test scores have a correlation coefficient of 0.85. What does this indicate about the relationship between study hours and test scores?

• Increased study hours lead to lower test scores.

• There is no correlation between study hours and test scores.

• There is a strong positive correlation between study hours and test scores.

• The correlation coefficient indicates a weak negative correlation.

In a survey, the correlation coefficient between the amount of rainfall and the number of umbrellas sold is found to be -0.75. What can you infer about this relationship?

• Umbrella sales increase as rainfall decreases.

• There is no correlation between rainfall and umbrella sales.

• Increased rainfall leads to more umbrella sales.

• There is a strong negative correlation between rainfall and umbrella sales.

A researcher calculates the correlation coefficient between the temperature and ice cream sales, finding it to be 0.90. How would you interpret this result?

• There is a strong positive correlation between temperature and ice cream sales.

• The correlation indicates a weak negative relationship between temperature and ice cream sales.

• There is no correlation between temperature and ice cream sales.

• Ice cream sales decrease as temperature increases.

If the correlation coefficient between two variables is 0.0, what does this imply about their relationship? Provide an example of such variables.

• One variable causes changes in the other variable.

• There is no linear relationship between the two variables.

• There is a strong positive relationship between the two variables.

• The variables are perfectly correlated in a non-linear way.

A dataset shows a correlation coefficient of 0.65 between the number of hours spent on social media and students' grades. Calculate the correlation coefficient if the number of hours increases to 10 and grades improve significantly. What does this suggest?

• The correlation coefficient remains unchanged, showing no impact on the relationship.

• The correlation coefficient may increase, suggesting a stronger positive relationship.

• The correlation coefficient will decrease, indicating a weaker relationship.

• The correlation coefficient will become negative, suggesting an inverse relationship.

In a health study, the correlation coefficient between exercise frequency and body mass index (BMI) is -0.60. What does this suggest about the relationship between these two variables?

• There is a weak negative correlation; exercise has little impact on BMI.

• There is a moderate negative correlation; more exercise is associated with lower BMI.

• There is no correlation; exercise frequency does not affect BMI.

• There is a strong positive correlation; more exercise is associated with higher BMI.

A company finds a correlation coefficient of 0.95 between advertising spend and sales revenue. If they increase their advertising budget, what can they expect in terms of sales?

• They can expect a decrease in sales revenue.

• There will be no change in sales revenue.

• Sales revenue will fluctuate unpredictably.

• They can expect an increase in sales revenue.

The correlation coefficient between the number of books read and reading comprehension scores is 0.78. If a student reads more books, what can be inferred about their comprehension skills?

• If a student reads more books, it can be inferred that their comprehension skills are likely to be better.

• Increased reading leads to confusion in understanding texts.

• More books read indicates lower comprehension skills.

• Reading more books has no effect on comprehension skills.

A correlation coefficient of -0.40 is found between the number of hours spent watching TV and academic performance. What does this suggest about the impact of TV on students' grades?

• TV watching has no effect on students' grades.

• More TV watching leads to better academic performance.

• TV watching negatively impacts students' grades.

• TV watching improves focus and study habits.

If a correlation coefficient is calculated to be 1.0, what does this indicate about the relationship between the two variables? Provide a real-world example.

• The relationship between the two variables is random and unpredictable.

• For example, the relationship between temperature in Celsius and temperature in Fahrenheit is a perfect positive correlation, where an increase in Celsius results in a proportional increase in Fahrenheit.

• An increase in one variable leads to a decrease in the other variable.

• A correlation coefficient of 1.0 indicates no relationship between the variables.