Question

A suoervisor of a manufacturing plant is interested in relating the average number of defects produced per day to two factors: the operator working the machine and the machine itself. The supervisor randomly assigns each operator to use each machinefor three days andrecords the number of defects produced per day. The results of the study are shown in the table below. Perform a hypothesis test to test if there is any interaction between machine and operator variables. State the null and alternative hypothesis and determine if you require a one way or a two ANOVA table. Create the required ANOVA table using Analysis ToolPak. Use α = 0.10. State the decision rule and the decision of the test. Based on your decision statement can one perform an F-test to test the effect of machine types on average number of defects?
						Number of defects produced per day
							Operator A	Operator B	Operator C
						Machine A	3	7	3
							3	5	2
							3	3	1
						Machine B	2	6	2
							2	4	1
	2	2	0
Machine C	1	5	1
	1	3	0
	1	2	1
H0:
Ha:
Decision rule
Decision statement
Test for machine type of number of defects

Answer 1

i over all mean is, x = 1.75 1.8 up Hai MA= MB = Mei Hai means are not equal , a=0.10 test statics is Erstatistic for annova F = MSB/msE set decision rule, Determine Critical Value off we he degrees of freedom dibiakol @ dfe EN-K, dil,- K-1-3-1=2 difaz NK= 12-3=9 The critical value is 3.01 & deusion rule follows: Reject to if f> 3:01 need is as Test statistics A B ni = 3 1₂ = 3 nu-3 X = 4 X2 २ *3 = 1

SSB = Enj - Z :. SSB = 3(4 – 1-8) 1.8) 73(2-18)+3 1-15) 14-5at 1.93 16.56 SSE.EE (x - 1)? Se requires mputing the squared between observations & its groupmean. Com a terme caib А (x-u) 2 (x-4) 3 E j 늦 3 ws Thus, Elx-x) ² - 3 (x-2) (x-2)² A home 2 2 o E(X- X2 ) 2 0/ Cx-D НА (x-1)- 6 ECx -x20

Therefore, SSE EE (X-M) 3+0+0 311 ,, ANNOVA table (mearsquares Source SS dif mis of Venahan Between treatment 16.56 16.562, F-8:23 3/470:33 =25.09 :628 0.33 Errerfor Residual) 3 12-39 Total 12'-!! Here, we reject Ho because, 25.097, 3:01 we have statistically significant evidenie of x=0:05. There is significant difference between the the interaction & operator Here, from f-test, fa 25.09. machine