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# Probability Distribution and P-Values

A supermarket advertises that the waiting time spend by customers waiting in line at the cash register is uniform between 0 and 6 minutes. A number of customers complain that they wait in line too long for this to be true. Joel, the manager, decides to test whether the complains are justified by testing the hypotheses:

Ho: µ = 3
H1: µ > 3

a) Sketch the distribution of waiting time when Ho is true. Be sure to label and give appropriate values on the axes.

b) One possible decision rule for Joel is to reject Ho if the next randomly chosen customer waits in line longer than 5 minutes. What is the chance of a Type I error using this decision rule?

c) Suppose the next randomly chose customer waits in line 5.5 minutes. What is the corresponding p-value? Using the significance level from part b, what is the decision and conclusion?

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Question 3:

A supermarket advertises that the waiting time spend by customers waiting in line at the cash register is uniform between 0 and 6 minutes. A number of customers complain that they wait in line too long for this to be true. Joel, the manager, decides to test whether the complains are justified by testing the hypotheses:

Ho: µ = 3
H1: µ > 3

a) Sketch the distribution of waiting time when Ho is true. Be sure to label and give appropriate values on the axes.

The problem says that the distribution is uniform. That means that the probability of waiting for any amount of time between 0 and 6 minutes is constant. A uniform probability distribution looks like ...

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