4. (Please show the work in text. Thank you,) A test of H₀: p = 0.4 versus H_a: p > 0.4 has the test statistic z = 2.52. 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? (4 points)

5. At a Bloomburg City Council meeting, a plan to fund more swim safety programs was presented. The reasoning behind the request was that less than 40% of children under the age of 5 could pass a swim test. If this is true, the council will agree to fund more programs for these kids. The council decides to take a 200-person volunteer sample of children under 5 years in Bloomburg City and conduct a significance test for H0: p = 0.40 and Ha: p < 0.40, where p is the proportion of these children that can pass a swim test. They will perform a significance test at a significance level of = 0.05 for the hypotheses. Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points) Part B: Out of the 200 children under 5 that volunteered to take a swimming test, 87 passed, resulting in a p-value of 0.8438. What can you conclude from this p-value given the data of the 200 children is sufficient to perform a significance test for the hypotheses? (4 points) Part C: What possible defect in the study can you find in Part B? Explain. (3 points)