Correlation Coefficient Worksheets Grade 11

1. Emma, a botanist, is studying the relationship between the number of hours of sunlight per day and the height (in cm) of a particular species of plant after 30 days. She collects data from 9 plants and calculates the Pearson correlation coefficient, finding r = -0.73. Interpret this correlation coefficient in the context of the study, describing both the strength and direction of the linear relationship between sunlight hours and plant height.
2. Mere, a kaitiaki (environmental guardian), is studying the relationship between the age of a native forest (in years since regeneration began) and the number of endemic bird species observed in that forest. She collects data from 10 forest plots and calculates the following summary statistics: the mean age of the forests is 45 years, the mean number of bird species is 18, the standard deviation of age is 12 years, the standard deviation of bird species is 5, and the sum of the products of z-scores (Σzₓzᵧ) is 6.3. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between forest age and endemic bird species count.
3. Noah, a soil scientist, is studying the relationship between the organic matter content (as a percentage of dry soil mass) and the water holding capacity (in milliliters of water per 100 grams of soil) for 11 different soil samples. He calculates the following summary statistics: the mean organic matter content is 8.5%, the mean water holding capacity is 42 mL/100g, the standard deviation of organic matter is 2.2%, the standard deviation of water holding capacity is 9.6 mL/100g, and the sum of the products of the z-scores (Σzₓzᵧ) is 8.8. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between organic matter content and water holding capacity.

…and 2 more problems

1. Mason, a hydrologist, is studying the relationship between the depth of a river (in meters) at a specific point and the water flow velocity (in meters per second) at that same point. He collects data from 12 different river locations and computes the following summary statistics: the mean depth is 2.7 meters, the mean velocity is 1.2 meters per second, the standard deviation of depth is 0.7 meters, the standard deviation of velocity is 0.4 meters per second, and the sum of the products of the z-scores (Σzₓzᵧ) is 7.7. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between river depth and water flow velocity.
2. Tane, a sports scientist, is studying the relationship between the number of hours of sleep an athlete gets per night (x) and their reaction time in milliseconds (y) for 12 athletes. He collects the data and calculates the Pearson correlation coefficient, finding r = -0.71. Interpret this correlation coefficient in the context of the study, describing both the strength and direction of the linear relationship between sleep hours and reaction time.
3. Matiu, a marine biologist, is investigating the relationship between water temperature (°C) and the number of fish observed per hour at a reef. He records data at 10 different times and calculates a Pearson correlation coefficient of r = 0.92. Interpret this correlation coefficient in the context of the study, including both the direction and strength of the linear relationship.

…and 2 more problems

1. Emma, a sports scientist, is studying the relationship between the number of hours of training per week and the time (in seconds) to complete a 100-meter sprint for 12 athletes. She calculates the Pearson correlation coefficient and finds r = -0.85. Interpret this correlation coefficient in the context of the study, describing both the strength and direction of the linear relationship between training hours and sprint time.
2. Charlotte, an environmental scientist, is studying the relationship between the average daily temperature (in degrees Celsius) and the number of mosquitoes trapped per night in a wetland area. She collects data from 7 different nights and records the following summary statistics: the mean temperature is 22 degrees Celsius, the mean number of mosquitoes is 137, the standard deviation of temperature is 7 degrees Celsius, the standard deviation of mosquitoes is 12, and the sum of the products of the z-scores (Σzₓzᵧ) is 5.2. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between average daily temperature and mosquito count.
3. Mere, a marine ecologist, is studying the relationship between the surface water temperature (in degrees Celsius) and the concentration of dissolved oxygen (in mg/L) in a coastal estuary. She collects data from 13 different sampling stations and calculates the following summary statistics: the mean water temperature is 18.5°C, the mean dissolved oxygen concentration is 7.2 mg/L, the standard deviation of temperature is 3.2°C, the standard deviation of dissolved oxygen is 1.5 mg/L, and the sum of the products of the z-scores (Σzₓzᵧ) is 11.2. Compute the Pearson correlation coefficient r, and interpret the strength and direction of the linear relationship between water temperature and dissolved oxygen concentration.

…and 2 more problems