Problem (1): Process Control Distribution of Diameters Machine 1 Machine 2 X: Diameters(cm) The following samples were collected by measuring the diameter (cm) of corks intended for use in wine bottles from two different cutting machines. Machine 1 7.58 7.42 7.56 7.6 7.33 8.44 7.98 8.25 Machine 2 8.67 8.09 8.48 7.78 7.01 7.74 8.07 The production is said to be under control if the true (population) variance of the corks' diameters is equal to .25 cm². a. Conduct a hypothesis test to check if the variability of the diameters of the two machines is under control. b. Determine whether the variability of corks in machine 1 is less than in machine 2.
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$X_1 = \{7.58, 7.42, 7.56, 7.6, 7.33, 8.44, 7.98, 8.25\}$ $X_2 = \{8.67, 8.09, 8.48, 7.78, 7.01, 7.74, 8.07\}$ Calculate the sample variances for both machines. Show more…
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