Correlation vs Causation Worksheets Grade 11

1. Olivia is a data analyst for a national park service. She analyzes data from 75 forest regions and finds a strong positive correlation (r = 0.73) between the number of campfires reported each month and the number of search-and-rescue operations conducted that month. The park director proposes a new policy to ban all campfires, arguing that campfires directly cause hikers to get lost and require rescue. Explain why the director's causal conclusion is likely flawed and identify a plausible confounding variable that could explain this correlation.
2. A study of 27 coastal towns finds a Pearson correlation coefficient of r = 0.82 between the number of beach umbrellas sold (x) and the number of sunburn cases (y) in July. The mean of x is 62 with standard deviation 12, and the mean of y is 37 with standard deviation 7. Calculate the slope of the least-squares regression line for predicting sunburn cases from beach umbrella sales, then explain why this strong correlation does not imply that beach umbrellas cause sunburns.
3. Mere collects data from 15 schools on the number of hours of weekly music practice (x) and the average GPA (y) of students. The Pearson correlation coefficient is r = 0.82. The mean of x is 6.5 hours with standard deviation 2.4 hours, and the mean of y is 3.2 with standard deviation 0.6. Calculate the slope of the least-squares regression line for predicting GPA from music practice hours. Then, explain why this strong correlation does not imply that more music practice causes higher GPA.

…and 2 more problems

1. A study of 14 coastal towns finds a Pearson correlation coefficient of r = 0.91 between the number of beach umbrellas rented (x) and the number of jellyfish stings reported (y) in August. The mean of x is 120 with standard deviation 15, and the mean of y is 45 with standard deviation 9. Calculate the slope of the least-squares regression line for predicting jellyfish stings from beach umbrellas rented, then explain why this strong correlation does not imply that renting beach umbrellas causes jellyfish stings.
2. Matiu collects data from 14 coastal towns on the number of beach umbrellas rented (x) and the number of jellyfish stings reported (y) in July. The Pearson correlation coefficient is r = 0.82. The mean of x is 62 with standard deviation 11, and the mean of y is 38 with standard deviation 9. Calculate the slope of the least-squares regression line for predicting jellyfish stings from beach umbrellas rented. Then, explain why this strong correlation does not imply that renting beach umbrellas causes jellyfish stings.
3. Emma is a researcher studying the relationship between the number of hours students spend practicing a musical instrument per week and their scores on a standardized mathematics test. She collects data from 150 high school students and calculates a Pearson correlation coefficient of r = 0.55. The school board, upon seeing this result, proposes a policy requiring all students to spend at least 5 hours per week practicing an instrument, arguing that music practice directly improves math performance. As a critical thinker, explain why the school board's causal conclusion is flawed, and identify a plausible confounding variable that could explain the observed correlation.

…and 2 more problems

1. Noah collects data on the average daily temperature (in degrees Celsius) and the number of ice cream cones sold at a beachfront shop for 16 consecutive days in July. A scatter plot of the data shows a strong positive linear relationship. The correlation coefficient is r = 0.91. The regression line equation is ŷ = 11x + 21, where x represents the average daily temperature in degrees Celsius and ŷ represents the predicted number of ice cream cones sold. On a day when the average temperature was 26 degrees Celsius, the shop actually sold 306 ice cream cones. Based on this high correlation and the data, can we conclude that increasing the average daily temperature causes an increase in ice cream cone sales? Explain why or why not, referencing a potential confounding variable in this context.
2. Aroha, a data analyst for a national park service, has collected data from 35 different hiking trails. She finds a strong positive correlation (r = 0.79) between the number of trail markers installed on a trail and the number of visitor injuries reported on that trail over the past year. Based on this finding, a park manager suggests removing trail markers to reduce injuries. Explain why this causal conclusion is flawed, and identify a likely confounding variable that could explain the observed correlation.
3. Sophia, a data analyst for a large school district, examines the relationship between the number of books in a school's library and the average standardized test scores of its students. She collects data from 50 high schools and calculates a correlation coefficient of r = 0.78. The school board, upon seeing this strong positive correlation, immediately proposes a policy to double the number of books in every school library, claiming it will directly cause a significant increase in test scores. As a critical thinker, explain why the school board's causal conclusion is flawed. Identify a likely confounding variable that could explain the observed correlation, and describe what additional evidence or study design would be needed to establish a true causal relationship between library books and test scores.

…and 2 more problems