In: Statistics and Probability
A researcher hypothesizes that people who believe in paranormal phenomena will obtain higher scores on the personality dimension of openness-to-experience. To test this belief, the researcher takes 8 randomly-selected people and gives them 2 tests: one is a 50-item test that measures the extent to which they endorse beliefs in paranormal phenomena and the other is a 30-item test that measures their openness-to-experience. The following data were obtained:
| Subjects | Paranormal beliefs | Openness-to-experience | 
| 1 | 40 | 22 | 
| 2 | 20 | 14 | 
| 3 | 48 | 24 | 
| 4 | 6 | 9 | 
| 5 | 30 | 23 | 
| 6 | 26 | 20 | 
| 7 | 42 | 27 | 
| 8 | 12 | 7 | 
a) Do these data provide significant support for the researcher’s belief (α = .05)?
b) Use the data to generate a 95% prediction interval for the openness-to-experience score of a person with a paranormal beliefs score of 25.