Question

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed Complete parts (a) through (1) Patient 7 8 9 10 11 R Daily headache hours (before) 2.5 3.5 2.8 2.3 3.7 2.0 2.2 1.7 2.2 2.3 4.1 Daily headache hours after) 1.9 4.0 1.7 1.9 1.2 1.9 2.0 1.3 1.6 1.4 4.9 OD. Ho: Had OE Ho: Ha 50 OF HO:20 H:Ha> H: H0 Hoi Hy <a (b) Find the critical value(s) and identify the rejection region(s). (Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as needed.)

Answer 1

Giveni data Daily headache Dolby beadade di differena hours before) (s) hours (after) c) di = x;-yi Patient 2.5 1 0.6 2 3.5 J. 4.0 Jo 2 2.8 2.3 log 3.7 1-2 2.5 5 6 2,6 1.9 2.2 2.o 7 8 1.7 1.3 0.2 0.4 0-6 9 2.2 lo 2.3 4.9 -0,8 Edi= 6.t for sum = Edi= 6.1 Mean 6.L 3) 0.5545 sd = &cdi-a? n-1 (0.6-0.5545)² +- II- +(-0.8 - Or SJ45) ² 0.7347 sd = 0.8572

Hypothesis Hol eld so Vs Hi eld > o to-id=2.7638 critical valuess): tostnt a- tio. of tio, o. of 2.7638 df = 10 ( from t- table, one tailed, to = 2.7638 test statistic t= d solla O. SS4S-o 0.8572/51 te 2. 1454 Do decision cu t > critical to then Reject Ho otherwise not reject Ho 2.1454 L2.7638 j.e cal t < critical to then not reject Ho.

conclusion Do not reject Ho Then there is not enough evidence to conclude that soft tissue therapy helps reduce the length of tine patients suffer from headaches