A physical therapist suggests that soft tissue massage therapy helps to reduce the lengths of time patients suffer from headaches. The table shows the numbers of hours per day 18 patients suffered from headaches before and after 6 weeks of receiving treatment. At a = 0.05, is there enough evidence to support the therapist’s claim? Assume the populations are normally distributed.

For each exercise, perform the steps below.

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

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

(c) Find the critical value(s) and identify the rejection region(s).

(d) Find the appropriate standardized test statistic.

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

(f) Interpret the decision in the context of the original claim.

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Patient 3 4 5 6 5.2 5.2 Hours (before) 5.1 4.9 1.6 6.1 2.3 4.6 3.1 Hours (after) 2.5 3.5 3.3 3.7 2.3 2.7 2.4 2.1 2.8 15 Patient 10 11 12 13 14 16 17 18 Hours (before) 4.4 4.2 5.4 3.3 5.2 3.7 2.6 2.7 2.6 Hours (after) 4.1 3.0 2.4 2.4 2.7 2.6 2.4 2.7 2.4 2.