An herbal medicine is tested on 16 randomly selected patients with sleep disorders. Each patient's amount of sleep (in hours) is measured for one night with the herbal medicine and for one night without the herbal medicine. Researchers claim that the patients' condition will improve using the herbal medicine. At the 1% significance level, does the data support the researchers' claim? Patient Without With 1 1.8 3.0 2 2.0 3.6 3 3.4 4.0 4 3.5 4.4 5 3.7 4.5 6 3.8 5.2 7 3.9 5.5 8 3.9 5.7 9 4.0 6.2 10 4.9 6.3 11 5.1 6.6 12 5.2 7.8 13 5.0 7.2 14 4.5 6.5 15 4.2 5.6 16 4.7 5.9 15. Do women have a better vocabulary than men? Ten married couples are chosen at random and a vocabulary test is given to each of the husbands and each of the wives. Here are the scores: Men 68 76 74 91 84 70 77 82 92 69 Women 73 81 73 89 88 79 81 88 92 80 (cont. on next page) Mean (Without-With) = -1.525 S.d. (Without-With) = 0.542