Quality Control Inspector of a Supermarket - Entire Sydney Region - Statistics Assignment Help

Assignment Task :

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 Cut Weight.mtw. 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. 

1(a) Use Minitab to find the mean, standard error of the mean, standard deviation, minimum, Q1, median, Q3 and maximum of the weights of the 60 cuts of meat in the sample for each region and the overall in values for all 240 cuts in Sydney. Cut and paste the relevant Minitab output below.  

(b) Use Minitab to produce a histogram (with fit) of the distribution of cut weights for the entire Sydney region. Analyse the graph and comment on your findings.  

(c) What is the percentage of the cuts of meat in the entire Sydney sample that have a weight of at least 250 grams? 

(d) Based on the sample, find by hand a 95% confidence interval for the estimate of the percentage of the population of all such cuts of meat in Sydney that have a weight less than 250 grams. Would you believe that more than 45% of all such cuts of meat weigh less than 250 grams? Explain the reasons for your answer and show all working. 

(e) Find, by hand, a 95% confidence interval for the estimate of the mean weight of all cuts of meat in the chain across Sydney. Indicate whether they meet all the requirements of the inspector and therefore whether she should pursue the matter

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