Question

Step 2 of 2:

Make the decision to reject or fail to reject the null hypothesis of equal average number of defects produced per day for the different machines and state the conclusion in terms of the original problem. Be sure to test for interaction first. Use α=0.10α=0.10.

A supervisor 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 machine for three days and records the number of defects produced per day. Is there sufficient evidence to conclude that there is a significant difference among the average number of defects produced per day for the different machines? Number of Defects Produced per Day Operator A Operator B 3 8 Machine A C 3 2 Machine B 2 1 8 Machine C 8 ANOVA df MS Source of Variation 70.5833 2 35.2917 Machine 13.5000 13.5000 1 Operator 1.7500 2 0.8750 Interaction 152.0000 18 8.4444 Within 237.8333 23 Total Step 1 of 2: Find the value of the test statistic for testing the difference among the average number of defects produced per day for the different machines. Round your answer to two decimal places, if necessary. nswer 2 Points Tables Keypad F =

Answer 1

Step 1 ) Null hypothesis H0 : $\mu$_A = $\mu$_B = $\mu$_C

Alternative hypothesis H1 : At least one $\mu$ is different .

Test statistics F is

F = MS machine / MS within

F = 35.2917/8.4444

F = 4.18

Step 2) F critical for  $\alpha$ = 0.10 and d.f = ( 2,18)

F critical = F_{​​​​​​0.10, ( 2, 18) = 2.62}

_{Decision rule : if F > F critical we reject Ho , otherwise we fail to reject H0}

_{Our F = 4.18 > 2.62}

_{Decision : we reject the null hypothesis Ho.}

_{conclusion : There is sufficient evidence to conclude that there is significant difference among the average number of defects produced per day for the different machines.}