as np import pandas as pd from scipy.stats import pearsonr

Given data

x = np.array([21.4, 20.3, 16.9, 2.2, 25.6, 75.5, 28.2, 60.1, 4.6, 4.8, 0.4, 43.3, -3.8, 9.5]) y = np.array([37.8, 46.9, 87.6, 116.4, 68.9, -83, 29.6, -50.8, 138, 107.1, 136.8, -37.3, 122.3, 62.1])

(a) Calculate the correlation coefficient

correlation_coefficient, p_value = pearsonr(x, y)

Prepare results

correlation_coefficient_rounded = round(correlation_coefficient, 3) p_value_rounded = round(p_value, 3)

correlation_coefficient_rounded, p_value_rounded(a) The correlation coefficient for this data set is $r = -0.961$.

(b) The p-value for this correlation coefficient is $p = 0.000$.

(c) Your final conclusion is:

There is statistically significant evidence to support the claim that there is a correlation between the two variables in the population.

Do you want further explanations or have questions about the calculations? Here are 5 related questions to consider:

1. What does a correlation coefficient of $-0.961$ indicate about the relationship between the variables?
2. How is the p-value interpreted in the context of correlation significance testing?
3. Can the strength of a correlation differ depending on the scale of the data?
4. What would the results imply if the p-value had been higher than 0.05?
5. How can we visually assess correlation using a scatter plot?

Tip: Always visualize your data with a scatter plot to better understand the