Suppose that as a quality control consultant, you know the population of machine operators for a corporation has a processing time for a particular product that is normally distributed with a mean of 82 minutes. Your consulting firm has just developed a new training method for machine operators that you claim will decrease the amount of time it takes to process this particular product. Using the data from 15 randomly selected trainees, determine whether they perform significantly better than the population of machine operators trained using the traditional method. The sample of 15 randomly selected trainees had a mean time of 78.3 minutes and standard deviation of 5.2 minutes.

1. Set up the hypotheses for the test to determine if there is enough evidence to suggest the actual mean content differs from the stated value. Use appropriate symbols.

2. Calculate the value of the test statistic showing the work using the formula.

3. Determine the p-value using the t-distribution. Copy and paste the output from the statistical computing package that you use. Specify which one that you use. Attach on separate paper if necessary.

4. Make the decision for the hypothesis test in terms of the null hypothesis.