A health psychologist investigated whether a virtual-reality (VR) guided-breathing program is effective in reducing chronic lower-back pain intensity. Participants were randomly allocated to either a VR Breathing group (Na=6N_a = 6Na=6) or an Audiobook Control group (Nb=9N_b = 9Nb=9). Pain intensity was rated daily using an ordinal scale. The researcher conducted a Mann-Whitney U test and calculated an observed value of U=12U = 12U=12.
Table 1: Critical values for the Mann-Whitney U test
| NaN_aNa | Nb=5N_b = 5Nb=5 | Nb=6N_b = 6Nb=6 | Nb=7N_b = 7Nb=7 | Nb=8N_b = 8Nb=8 | Nb=9N_b = 9Nb=9 | Nb=10N_b = 10Nb=10 | Nb=11N_b = 11Nb=11 | Nb=12N_b = 12Nb=12 |
|---|---|---|---|---|---|---|---|---|
| p≤0.05p \le 0.05p≤0.05 (one-tailed) | ||||||||
| 6 | 6 | 8 | 11 | 13 | 15 | 17 | 19 | 21 |
Using the critical values for the Mann-Whitney U test in Table 1, explain whether the VR breathing program is effective in reducing pain intensity scores.
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