Home / Questions / At Farmer's Dairy, a machine is set to fill 32-ounce milk cartons However this machine doe...
At Farmer's Dairy, a machine is set to fill 32-ounce milk cartons. However, this machine does not put exactly 32 ounces of milk into each carton; the amount varies slightly from carton to carton. It is known that when the machine is working properly, the mean net weight of these cartons is 32 ounces. The standard deviation of the amounts of milk in all such cartons is always equal to .15 ounce. The quality control department takes a sample of 25 such cartons every week, calculates the mean net weight of these cartons, and makes a 99% confidence interval for the population mean. If either the upper limit of this confidence interval is greater than 32.15 ounces or the lower limit of this confidence interval is less than 31.85 ounces, the machine is stopped and adjusted. A recent sample of 25 such cartons produced a mean net weight of 31.94 ounces. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the amounts of milk put in all such cartons have a normal distribution.b. What is the probability that the population mean does not fall in the interval.c. Briefly explain how the width of a confidence interval decreases with an increase in the sample size, and also decreases with a decrease in the confidence level.d. Why do we always conduct a sample survey and not a census?
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