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A producer arranges his soup cans in boxes containing 24 cans, in the order in which they are produced. The weight of the packaging is a eristic feature essential: if it is too low, the producer violates the weights and measures law and exposes himself therefore to prosecution; if it is too high, the producer incurs additional costs (for extra soup and for those who are difficult to put lids on cans). The quality control of the production line consists of an EAS of n boxes; the 24 cans from each chosen can are then opened and the weight of the soup (in grams) in each can is measured. The resulting data is shown below, in the order in which the cartons were removed from the production line:

(a) Determine a C.I. (at about 95%) for the average weight of a can of soup. (b) It is suggested that an alternative to taking an EAS of boxes and examining all the cans in the chosen cans would have been to select an EAS of cans. Discuss the brief event of the pros and cons of this suggestion. (c) Using a scatterplot of average canned weights in a can depending on the order in which the boxes are chosen, briefly discuss the state statistical control of the can filling process. (d) Using the estimator yG, how many boxes had to be sampled in order to give an estimate of the average weight of the soup in all the cans of the cycle of production with a margin of error on the estimate of 0.2g? [It will first be necessary to a formula for determining sample size

Bote Poids moyen cart-type Boite Poids moyen cart-type 1 340.6 0.27 6 340.5 0.61 2 310.8 0.39 7 310.2 0.31 3 340.5 0.24 8 340.3 0.50 4 340.1 0.43 9 340.0 0.22 5 340.8 0.34 10 339.7 0.44 Bote Poids moyen cart-type Boite Poids moyen cart-type 1 340.6 0.27 6 340.5 0.61 2 310.8 0.39 7 310.2 0.31 3 340.5 0.24 8 340.3 0.50 4 340.1 0.43 9 340.0 0.22 5 340.8 0.34 10 339.7 0.44

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