Four different machines, M, M2, M3, and M4, are to be considered in assembling of a...

 

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Four different machines, M₁, M2, M3, and M4, are to be considered in assembling of a particular product. It is decided that six different operators are to be used in a randomized block experiment to compare the machines. The machines are assigned in a random order to each operator. The operation of the machines requires a certain amount of physical dexterity, and it is anticipated that there will be a difference among the operators in the speed with which they operate the machines (table below). The times, in seconds, were recorded for assembling the given product:< ( Machine 1 2 3 4 Total 1 42.5 39.8 40.2 41.3 163.8 2 39.3 40.1 40.5 42.2 162.1 3 Operator 4 5 6 39.6 39.9 42.9 40.5 42.3 42.5 41.3 43.4 44.9 43.5 44.2 45.9 164.9 169.8 176.2 174.1 43.6 43.1 45.1 42.3 Total 247.8 248.3 255.4 259.4 1010.9 r a) Fill up the blank of the above analysis of variance table.< Source of Variation Machines Operators Error Total J J Degree of freedom Sum of Squares 15.93 42.09 23.84 81.86 2 A Means sums square E 2 F F.05 J 2 b) Test the hypothesis H'o at the 0.05 level of significance that the machines perform at the same mean rate of speed. < c)Test the hypothesis H'o at the 0.05 level of significance that the operators perform at the same mean rate of speed. < P K E Four different machines, M₁, M2, M3, and M4, are to be considered in assembling of a particular product. It is decided that six different operators are to be used in a randomized block experiment to compare the machines. The machines are assigned in a random order to each operator. The operation of the machines requires a certain amount of physical dexterity, and it is anticipated that there will be a difference among the operators in the speed with which they operate the machines (table below). The times, in seconds, were recorded for assembling the given product:< ( Machine 1 2 3 4 Total 1 42.5 39.8 40.2 41.3 163.8 2 39.3 40.1 40.5 42.2 162.1 3 Operator 4 5 6 39.6 39.9 42.9 40.5 42.3 42.5 41.3 43.4 44.9 43.5 44.2 45.9 164.9 169.8 176.2 174.1 43.6 43.1 45.1 42.3 Total 247.8 248.3 255.4 259.4 1010.9 r a) Fill up the blank of the above analysis of variance table.< Source of Variation Machines Operators Error Total J J Degree of freedom Sum of Squares 15.93 42.09 23.84 81.86 2 A Means sums square E 2 F F.05 J 2 b) Test the hypothesis H'o at the 0.05 level of significance that the machines perform at the same mean rate of speed. < c)Test the hypothesis H'o at the 0.05 level of significance that the operators perform at the same mean rate of speed. < P K E