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A firm wishes to compare four programs for training workers to perform a certain manual task. Twenty new employees are randomly assigned to the training programs, with 5 in each program. At the end of the training period, a test is conducted to see how quickly trainees can perform the task. The number of times the task is performed per minute is recorded for each trainee, with the following results: Observation Program 1 Program 2 Program 3 Program 4 10 12 12 13 13 10 Using the hypothetical data provided below, test at a - 0.05 whether the four training programs are equally effective. What assumptions are necessary for your test?

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n fven Table obcesvation Progyan (0 12 Iy l0 13 Estimate the teatment effects stho fous pvogame Treatment effects SSR 4.95 96 53 0 5691352 -Ho :these is not sgríM-fCant defference between .teo Dogramm Ha: Thuse is a inifiant ditference befeoeen the program ANOVA table source df s F pvalu Treot ment S3 18-31 oG 0-03 Tota? 76s12 TRP-Valta δf F fest is 0.0031 So we an concede Heat thePu

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