In: Statistics and Probability
1. You are provided a sample of data on a criterion variable Y and predictor variable X for which 4 distinct subgroups can be identified. Based on these data, you calculate the sample correlation coefficients in the table to the right ==>
| Group | Sample Corr. Coeff. | Sample Sizes |
| 1 | 0.215 | 97 |
| 2 | 0.351 | 86 |
| 3 | 0.277 | 73 |
| 4 | 0.591 | 91 |
| Provide a test of the null hypothesis that the population correlation coefficients are equal across these four groups against the alternative the H0 is not true: |
| a. Calculated Chi-Square statistic |
| b. Critical (upper) Chi-Square for α=5% |
| c. Conclusion for α=5% |
| d. Critical (upper) Chi-Square for α=1% |
| e. Conclusion for α=1% |