) A cosmetics company fills its best--selling 8--ounce jars of facial cream by an automatic dispensing machine. The machine is set to dispense a mean of 8.1 ounces per jar. Uncontrollable factors in the process can shift the mean away from 8.1 and cause either underfill or overfill, both of which are undesirable. In such a case the dispensing machine is stopped and recalibrated. Regardless of the mean amount dispensed, the standard deviation of the amount dispensed always has value 0.22 ounce. A quality control engineer routinely selects 30 jars from the assembly line to check the amounts filled. On one occasion, the sample mean is xbar=2 ounces and the sample standard deviation is s = 0.25 ounce. Determine if there is sufficient evidence in the sample to indicate, at the 5% level of significance, that the machine should be recalibrated. Start by stating the null and alternative hypothesis. Perform a one sample hypothesis test. Report the test statistic and state whether you retain or reject the null and why. What is your conclusion about the recalibration of the machine? 12 Points