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.