Formulating a hypothesis and classifying the type of error
A manufacturer of stereo systems has a production line that produces an average of 100 stereo systems per day. Because of new government regulations, a new safety device has been installed, which the manufacturer believes will reduce average daily output. A sample of 49 days output after the installation of the safety device yielded an average output per day of 99.2 systems, with a sample standard deviation 4.85.
a) Formulate the appropriate null and alternative hypotheses to test the manufacturer's belief.
b) At the 5% level of significance, is there sufficient evidence to support the manufacturer's belief? Draw a graph of your rejection region. In no more than one sentence, explain.
c) Which type of error, a Type I or Type II, would you be vulnerable to in interpreting this test? In no more than a single sentence, describe the practical implications of committing this error.
d) Using the sample mean of 99.2, compute a 90% confidence interval. Show the computation, and interpret in one sentence the interval you compute.