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Suppose that the average trip time from Oak Park to UIC on the Blue line is 23 minutes and that the standard deviation of the population is 4 minutes (sigma=4). We are interested to know whether the average trip time on Thursdays is shorter. We study a sample of 49 trips on Thursdays and the average is 21.25 minutes. Execute a hypothesis test at alpha= 1% that the average trip time on Thursdays is shorter (that is, that it requires a smaller number of minutes). State Ho, Ha, calculate the appropriate statistic, p-value, state whether you reject Ho vs. not and state your conclusion in plain English. You must use the p-value method taught in class. If you use the critical value method, then you will receive 0 points for this part of the problem. Show all work.
What is the largest number of minutes that will allow you to reject Ho?
What is the probability that you will reject Ho if mu is actually 22 minutes?
Fill in the probabilities in the table below. Also indicate alpha, beta and power.
What test concludes Ho is true in population Ho not true in population
Reject Ho
Not reject Ho
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