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1) A test of H₀: p = 0.4 versus H_a: p > 0.4 has the test statistic z = 2.52. (10 points) Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points) Part B: If the alternative hypothesis is H_a: p 0.4, what conclusion can you draw at the 5% significance level? At the 1% significance level?

2) A study is performed involving two therapies for people unable to walk from severe pain due to arthritis. In the study, 300 individuals were randomly given one of two therapies. Specifically, 125 were given Therapy A and 175 were given Therapy B. A total of 88 of the 300 individuals were able to walk with little to no pain, 32 from Therapy A group and 56 from Therapy B group. (10 points) A significance test was performed for the following hypotheses resulted in a p-value of 0.1150: H₀: Walking rates are the same for Therapy A and B H_a: Therapy B has a greater walking rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of errorType I or Type IIcould have been made? What is one potential consequence of this error? (3 points)