A specialized medical clinic operates under the assumption that the mean patient wait time is 35.035.035.0 minutes, with wait times following a normal distribution. A regulatory body suspecting inefficiency believes that the mean wait time, μ\muμ, has increased. To investigate, they audit 16 randomly selected patient records, yielding a sample mean wait time of wˉ=37.3\bar{w} = 37.3wˉ=37.3 minutes and a sample standard deviation of s=5.2s = 5.2s=5.2 minutes.
Stating your hypotheses clearly, test at the 5% significance level whether or not there is sufficient evidence to support the regulatory body's suspicion.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.