Filling machines. A company uses six filling machines of the same make and model to place

detergent into cartons that show a label weight of 32 ounces. The production manager has

complained that the six machines do not place the same amount of fill into the cartons. A

consultant requested that 20 filled cartons be selected randomly from each of the six machines

and the content of each carton carefully weighed. The observations (stated for convenience as

deviations from 32.00 ounces) follow. Assume that ANOVA model (16.2) is applicable.

7

2

3

. . .

BL

19

20

aLAWN-

-.14

.20

07

. . .

07

-.19

46

11

12

. .

02

.11

.12

21

78

.32

. . .

.50

20

61

49

58

52

. . .

.42

.45

20

-.19

27

.06

. . .

14

35

-.18

05

-.05

28

. . .

35

-.09

:05

a. Prepare aligned box plots of the data. Do the factor level means appear to differ? Does the

variability of the observations within each factor level appear to be approximately the same

for all factor levels?

b. Obtain the fitted values.

c. Obtain the residuals. Do they sum to zero in accord with (16.21)?

d. Obtain the analysis of variance table.

c. Test whether or not the mean fill differs among the six machines: control the o risk at .05.

State the alternatives. decision rule. and conclusion. Does your conclusion support the

production manager's complaint?

F. What is the P-valuc of the test in part (e)? Is this value consistent with your conclusion in

part (e)? Explain.

g. Based on the box plots obtained in part (a), does the variation between the mean fills for

the six machines appear to be large relative to the variability in fills between cartons for

any given machine? Explain.

Ley =0 i=1...,r

(16.21)

The ANOVA model can now be stated as follows:

Yi = Mitzi

(16.2)