Question

Provide an appropriate response.

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Test the significance of the correlation coefficient using a = 0.05 and the claim q=0.
Number of absences, x: 4,7,10,8,13,6,19,12,9
Final Grade, y: 95,83,77,79,68,89,52,73,79

Answer 1

We reject the null hypothesis due to a p-value of 0.026, which is less than the significance level of 0.05, indicating a significant correlation between absences and final grades.

Step-by-step explanation:

To determine if there is a significant correlation between the number of absences (x) and final grades (y), we can perform a hypothesis test. The null hypothesis states that there is no correlation (ρ=0), while the alternative hypothesis suggests a significant correlation exists (ρ≠0).

Given the low p-value of 0.026, which is less than the significance level (α) of 0.05, we reject the null hypothesis. This means there is sufficient evidence to conclude that a significant linear relationship exists between the number of absences and the final grades. Therefore, the correlation coefficient is significantly different from zero, and the regression line can be used for prediction.