Q1. The following table presents the list of agencies owning different number of rental cars. The annual income for each of these agencies is given here. (Table content not included here)
- (a)) The study wanted to analyse whether there is any significant relationship between the number of rental cars that the agency owns and its annual income. Compute the correlation coefficient from the given table. (400 words)
- (b)) Test the significance of the correlation coefficient considering α=0.05 and critical values obtained from t-distribution table is ±2.776 (400 words)
Key Points:
- Pearson's correlation coefficient (r) quantifies the strength and direction of a linear relationship between two quantitative variables.
- The formula for 'r' requires sums of X, Y, X², Y², and XY, along with the number of observations (n).
- A correlation coefficient close to +1 indicates a strong positive linear relationship, where both variables increase together.
- The significance of the correlation coefficient is tested using a t-distribution with n-2 degrees of freedom.
Answer: To analyze the relationship between the number of rental cars an agency owns and its annual income, we employ correlation and hypothesis testing. First, Pearson's product-moment correlation coefficient is computed to quantify the strength and direction of the linear relationship. Subsequently, a t-test is performed to assess the statistical significance of this correlation, determining if the observed relationship is likely due to chance or represents a true association in the population.