Question 1
The quality control inspector of a supermarket chain based in Sydney has the task of checking on the weights of various cuts of meat for sale in the freezer. They are labelled as ‘net weight 250 grams’ although they are cut by a machine that may not be entirely accurate. She has recently heard reports that several customers who shop in the chain are becoming increasingly dissatisfied and suspicious that some of the meat does not adequately meet the displayed weight. Although some leeway is tolerated in the weights, if they are too light (customer paying too much) or too heavy (store loses money) then serious problems may arise for the chain management. This means, of course, that some meat may be under specifications and some may be over specifications, but the overall mean weight of all such cuts of meat should be very close to the specified weight. Any inaccuracy is due to the fact that the cutting process itself is subject to variation.
The inspector assures the complaining customers that the weights of the meat will be checked, but she clearly does not have time to weigh them all. To get a preliminary idea on any possible problems, she selects a random sample of 60 cuts of meat from supermarkets in the chain from each of the four regions of Sydney (East, West, North and South) These meats are ideally supposed to have a weight of 250 grams. She weighs each cuts of meat in the sample and records the weight. These 240 weights are given in C1 of the Minitab worksheet T3 2020 Cut Weight.mtw that may be downloaded from the IDA website. Column C2 of the worksheet shows the region from which the meat was sampled.
The instructions from management is that she is to calculate, based on the sample, a 95% confidence interval for the population mean weight of all cuts of meat on sale in the supermarket chain. This confidence interval must meet all three of the following requirements:
• It must contain 252.00 grams
• It must not contain 255.00 grams
• It must not contain 245.00 grams
If these requirements are not all met, the inspector must launch an immediate investigation by measuring the weight of every cut of meat on sale during the coming six months – a process that will be very time consuming and expensive for the supermarket chain. On the other hand, if the above requirements are all met, she is to report that the meat weights are within acceptable limits (although there may be some outside) and she will not pursue the matter further for the time being.
Answer the following questions.
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