TIUULU . A Bottle-Filling Machine Is Set To Dispense 16.0 Fluid Ounces Into Soda Bottles. To Ensure That The Machine Is Filling Accurately, Every Hour A Worker Randomly Selects Four Bottles Filled By The Machine During The Past Hour And Measures The Contents. If There Is Convincing Evidence That The Mean Amount Of Juice Dispensed Is Different From 12.1

 

A bottle-filling machine is set to dispense 16.0 fluid ounces into soda bottles. To ensure that the machine is filling accurately, every hour a worker randomly selects four bottles filled by the machine during the past hour and measures the contents. If there is convincing evidence that the mean amount of juice dispensed is different from 12.1 ounces or if there is convincing evidence that the standard deviation is greater than .05 ounce, the machine is shut down for recalibration. It can be assumed that the amount of juice that is dispensed into bottles is normally distributed. During one hour, the mean number of fluid ounces of 5 randomly selected bottles was 16.1 and the standard deviation was .079. a) Perform a test of significance to determine whether the mean amount of soda dispensed is different from 16.0 fluid ounces. b) To determine whether this sample of 5 bottles provides convincing evidence that the standard deviation of the amount of soda dispensed is greater than 0.05 fluid ounces, a simulation study was performed. In the simulation study, 300 samples, each of size 5, were randomly generated from a normal population with a mean of 16.0 and standard deviation 0.05. The sample standard deviation was computed for each of the 300 samples. The dotplot below displays the values of the sample standard deviations. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Use the results of this simulation study to explain why you think the sample provides or does not provide evidence that the standard deviation of the soda dispensed exceeds 0.05 fluid ounce.