import numpy as np import matplotlib.pyplot as plt from scipy.stats import pearsonr

Data

overhead_width = np.array([7.1, 7.5, 9.9, 9.3, 8.7, 8.4]) weights = np.array([112, 161, 251, 200, 199, 191])

Scatterplot

plt.figure(figsize=(8, 6)) plt.scatter(overhead_width, weights, color='blue', edgecolor='black') plt.title('Scatterplot of Overhead Width vs Weight') plt.xlabel('Overhead Width (cm)') plt.ylabel('Weight (kg)') plt.grid(True) plt.show()

Correlation coefficient

r, _ = pearsonr(overhead_width, weights)

Critical value for alpha = 0.01 and n=6

n = len(overhead_width) critical_values = {4: 0.99, 5: 0.959, 6: 0.917, 7: 0.875} critical_value = critical_values[n]

r, critical_value/tmp/ipykernel_12/4001100189.py:11: UserWarning: You passed a edgecolor/edgecolors ('black') for an unfilled marker ('x'). Matplotlib is ignoring the edgecolor in favor of the facecolor. This behavior may change in the future. plt.scatter(overhead_width, weights, color='blue', edgecolor='black')

<<ImageDisplayed>>(0.9499211878781388, 0.917)(0.9499211878781388, 0.917)successThe calculated linear correlation coefficient $r$ is approximately 0.950 (rounded to three decimal places).

The critical value of $r$ for $n = 6$ and $\alpha = 0.01$ is 0.917. Since $|r| = 0.950$ is greater than the critical value of 0.917, there is sufficient evidence to reject the null hypothesis $H_0: \rho = 0$.

Conclusion:

There is significant evidence to conclude that there is a linear correlation between the overhead widths of seals and their weights.

Would you like me to assist further with interpretation, or do you have questions about this process?

Here are 5 related questions:

1. What does the correlation coefficient $r$ indicate about the relationship between width and weight?
2. How would the critical value change if the sample size were larger?
3. What are the assumptions of the Pearson correlation test?
4. Can we use this correlation for prediction? Why or why not?
5. How would outliers affect the correlation coefficient in this scenario?

Tip: A correlation does not imply causation; always examine the context of the data!