Final answer:
To determine the correlation coefficient's strength and whether it's significant, we look at its value and the p-value. A correlation coefficient close to -1 or +1 indicates a strong relationship. If p is less than 0.05, the correlation is significant and the regression line can be used for prediction.
Step-by-step explanation:
The calculation of the correlation coefficient (r) is a common task in statistics when we want to determine the strength and direction of the linear relationship between two variables. In the context of the provided data, the student is required to calculate the correlation coefficient using the hours spent studying and the test scores. The significance of this correlation is assessed by the p-value, which is a measure of the probability that the observed correlation occurred by chance assuming the null hypothesis (no correlation) is true.
To determine the strength of the model, we look at the correlation coefficient's value in relation to -1 and +1. The closer the correlation coefficient is to these extremes, the stronger the relationship. Additionally, we check whether the calculated correlation is significantly different from zero by looking at the p-value and comparing it to a significance level (commonly α = 0.05). If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is significant evidence to suggest a relationship between the variables.
For instance, if we compute a correlation coefficient of 0.801 with a sample size of 10, and reference Table 12.9 indicating a critical value of ±0.632 for 8 degrees of freedom, our r-value of 0.801 is greater than 0.632. Thus, the correlation is deemed significant, and the regression line may be used for predictions.