A researcher is investigating whether there is a linear correlation between the number of hours studied and exam scores among a group of students. The data collected and the corresponding scatterplot are as follows:

Calculate the value of the linear correlation coefficient $r$ and determine the critical values of $r$ at a significance level of $\alpha =0.05$. Is there sufficient evidence to support the claim that there is a linear correlation between hours studied and exam scores?

Use the ranks from the data provided below to calculate the Spearman rank correlation coefficient. Then, using a $0.05$ significance level, find the critical value and determine whether there is a statistically significant correlation between the two variables.

The following table lists sound quality rankings and prices (in dollars) for different brands of wireless earbuds (based on hypothetical data). Lower values of the sound quality rankings correspond to better audio performance.

Use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of $\alpha =0.05$. Do the more expensive brands appear to have better sound quality?