Calculate Pearson’s correlation coefficient, 𝑟, from raw data using technology, and interpret it to quantify the strength of a linear association.

Calculate Pearson's correlation coefficient, $r$, for the data shown in the table below and use it to describe the strength of the linear association between weekly exercise time and resting heart rate.

A researcher collected data on the relationship between hours spent studying per week and performance on a standardized test (out of 100) for 12 students. The Pearson correlation coefficient calculated from this dataset is $r = -0.14$. Which statement best describes the strength and direction of the association between study hours and test performance?

A florist recorded the weekly spending on fresh flowers (in dollars) and the number of weekly customer visits for 8 consecutive weeks at a market stall. (a) Calculate Pearson's correlation coefficient, $r$, to 3 decimal places. [2 marks] (b) Using your result from part (a), describe the strength of the linear association between customer visits and spending. [1 mark]

A marine biologist is investigating whether the salinity level (parts per thousand, ppt) of coastal water influences the population density of barnacles (number per square metre). Data were collected from seven sampling sites along a coastline. Calculate Pearson's correlation coefficient for the dataset and interpret the value to describe the strength of the linear association between salinity and barnacle population density.

A wildlife biologist investigates whether the population of a native bird species can be predicted by the number of native trees planted in a region. Data were collected from eight regions over the past two years. Calculate Pearson's correlation coefficient, $r$, for the association between the number of native trees planted and the bird population. Then interpret this value to describe the strength of the linear association between these two variables.