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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.