Prepare a managerial report that addresses the following issues.
- Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p-value for each test.
- Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?
- Compute limits for the sample mean around 12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If the mean exceeds the upper limit or if the mean is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality control purposes.
- Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?