Twelve nursing students are set to graduate and the registration clerk at the nursing school wonders if there is a correlation between a student's age, their GPA and their state board score. She collects data about the 12 students. The data is given below. Test the null hypothesis that all coefficients are zero at the 95% confidence level.
Age
| GPA
| State
Board | | Age
| GPA
| State
Board |
| 26 | 3.0 | 620 | | 27 | 3.3 | 639 |
| 25 | 3.1 | 568 | | 25 | 3.5 | 558 |
| 30 | 2.3 | 633 | | 26 | 2.0 | 595 |
| 20 | 2.5 | 516 | | 20 | 3.2 | 511 |
| 23 | 3.9 | 585 | | 25 | 3.5 | 579 |
| 23 | 2.5 | 584 | | 23 | 4.0 | 566 |
◦ Fail to reject the null hypothesis.
◦ The probability plot of residuals indicates normality of residuals so the hypothesis test is inconclusive.
◦ The probability plot of residuals indicates non-normality of residuals so the hypothesis test is inconclusive.
◦ Reject the null hypothesis.
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