Because of tourism in the state, it was proposed that public schools in Michigan begin after Labor Day. To determine whether support for this change was greater than 65%, a public poll was taken. Let p equal the proportion of Michigan adults who favor a post–Labor Day start. We shall test H0: p = 0.65 against H1: p > 0.65.
(a) Define a test statistic and an α = 0.025 critical region.
(b) Given that 414 out of a sample of 600 favor a post–Labor Day start, calculate the value of the test statistic.
(c) Find the p-value and state your conclusion.
(d) Find a 95% one-sided confidence interval that gives a lower bound for p.