An operations manager at a metropolitan hospital is evaluating a new triage protocol designed to reduce patient wait times in the Emergency Department. Before the protocol was introduced, a random sample of 60 patients had a mean wait time of 142 minutes with a standard deviation of 32 minutes. After the protocol was implemented, a second random sample of 75 patients showed a mean wait time of 128 minutes with a standard deviation of 24 minutes.
Test at the 1% level of significance whether the mean wait time in the Emergency Department has decreased under the new protocol. State your hypotheses clearly.
Explain the importance of the Central Limit Theorem in the context of this hypothesis test.
State one assumption regarding the sample variances that was necessary to perform this test.
