1. Four different machines, M1, M2, M3, and M4, are being considered for the assembling of a particular product. It was decided that six different operators would be used in a randomized block experiment to compare the machines. The machines were assigned in a random order to each operator. The operation of the machines requires physical dexterity, and it was anticipated that there would be a difference among the operators in the speed with which they operated the machines. The amount of time ( n seconds) required to assemble the product are shown in the table. Test the hypotheses at the 0.05 level of significance, that the machine performs at the same mean rate of speed. Time, in seconds, to assemble product Operator Machine 1 2 3 4 5 6 1 42.5 39.3 39.6 39.9 42.9 43.6 2 39.8 40.1 40.5 42.3 42.5 43.1 40.2 40.5 41.3 43.4 44.9 45.1 A 41.3 42.2 43.5 44.2 45.9 42.3 Source of Degrees of Variation Sum of Squares Freedom Mean Square Fo Treatments SS Treatments a - SS Treatments MS Treatments MSE Blocks SSBlocks b - 1 SSBlocks b - 1 SSE Error SS, (by subtraction) (a - 1)(b - 1) (a - 1)(b - 1) Total SST ab - 1 Complete the table State the hypotheses Residual graphs of machine Residual graphs of operator 2. Four kinds of fertilizer f1, f2, f3, and fa are used to study the yield of beans. The soil is divided into 3 blocks, each containg 4 homogenous plots. The yield in kilograms per plot and the corresponding treatment are as follows. Conduct an analysis of variance at the 0.05 level of significance using the randomized compete block model. Block 1 Block 2 Block 3 f1 = 42.7 f3 = 50.9 f4 = 51.1 f3 = 48.5 fi = 50.0 f2 = 46.3 f4 = 32.8 f2 = 38.0 f1 = 51.9 fi = 39.3 f4 = 40.2 fa = 53.5 Source of Degrees of Variation Sum of Squares Freedom Mean Square Fo Treatments SS Treatments SSTreatmen MSTreatments MSE SSale Blocks SSmacks b - 1 Error SS, (by subtraction) (a - 1)b - 1) (a - 1)(b - 1) Total SS, ab - 1Complete the table State the hypotheses Residual graphs of fertilizer Residual graphs of weight