Question: Because of tourism in the state it was proposed that

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.

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