A company uses six lling 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 ll into the cartons. A consultant requested that 20 lled cartons be selected randomly from each of the six machines and the content of each carton carefu1ly weighed. The observations (stated for convenience as deviations from 32.00 ounces) follow. Assume that ANOVA model (16.2) is applicable. j
i 1 2 3 18 19 20
1 14 .20 .07 .07 .01 .19
2 .46 .11 .12 .02 .11 .12
3 .21 .78 .32 .50 .20 .61
4 .49 .58 .52 .42 .45 .20
5 .19 .27 .06 .14 .35 .18
6 .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.
e. Test whether or not the mean fill differs among the six machines; control the α risk at 05. State the alternatives, decision rule, and conclusion. Does your conclusion support the production manager's complaint?
f. What is the P-value of the test in part (e)? Is this valtue 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 the six machines appear to be large relative to the variability in fills between cartons for any given machine? Explain.