The Director of Transportation for Big State University has asked for your help in evaluating the usage of one of the university's larger parking facilities. A student government organization has made the claim that, on average, more than 1,500 cars enter
this facility each day. You have verified that they have correctly formulated the following hypothesis test:

H0: µ = 1,500
H1: µ > 1,500

Furthermore, you have been provided with the following random sample of data collected over a five-day period:

Day Number of Cars Entering Facility

1 1,545

2 1,499

3 1,612

4 1,508

5 1,578

You wish to perform this test such that ? = 0.05.

(a) Verify that all three methods of evaluating a hypothesis test yield the same conclusion for this test.

1. Critical region method

2. P-value method

3. Confidence interval method

(c) If the null hypothesis is true, then what is the probability of a Type I error?

(d) If the null hypothesis is false, then what is the probability of a Type I error?