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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.