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.