A physical therapist suggests that soft tissue therapy and spinal manipulation help to reduce the lengths of time patients suffer from headaches. The table shows the numbers of hours per day 11 patients suffered from headaches before and after 7 weeks of receiving treatment. At α = 0.01, is there enough evidence to support the therapist’s claim?

(a) Identify the claim and state H₀ and H_a,

(b) Find the critical value(s) and identify the rejection region(s),

(c) Calculate d̅ and s_d,

(d) Find the standardized test statistic t,

(e) Decide whether to reject or fail to reject the null hypothesis,

(f) Interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed. If convenient, use technology.

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Patient123 4 5 6 78 9 10 11 Hours 2.8 2.4 28 2.6 2.7 2.9 3.2 2.9 4.1 1.6 2.5 Hours after) 1.6 13 1.6 .4 1.5 1. 7 1.6 1.81.2 1.4