In the carbonated beverage industry, dispensing pressure can be an important factor in achieving accurate fill volumes. Too little pressure can slow down the dispensing process. Too much pressure can create excess "fizz" and, thus, inaccurate fill volumes. Accordingly, a leading beverage manufacturer wants to conduct an experiment at three different pressure settings to determine if differences exist in the mean fill volumes. Forty bottles with a target fill volume of 12 ounces were filled at each pressure setting, and the resulting fill volumes (in ounces) were recorded. A portion of the data is shown in the accompanying table.
Low Pressure (60 psi) Medium Pressure (80 psi) High Pressure (100 psi)
12.00.......................................12.00..............................11.56
11.97.......................................11.87..............................11.55
⋮................................................⋮....................................⋮
12.00.......................................12.14..............................11.80
a. Construct an ANOVA table.
b. Specify the competing hypotheses to test whether there are differences in the mean fill volumes across the three pressure settings.
c. At the 5% significance level, what is the conclusion of the test? What about the 1% significance level?