A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys and SRS of 200 students of the over 2500 students at the school. In all, 83 students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective. Perform a test of the principal’s claim at the α = 0.05 significance level but only answer the following questions below!
(a) Describe a Type I Error and a Type II Error in this setting, and explain the consequences of each.
(b) The test has a power of 0.75 to detect that p=0.045. explain what this means.
(c) Identify two ways to increase the power in part (b).