An article in the Fire Safety Journal (“The Effect of Nozzle Design on the Stability and Performance of Turbulent Water Jets,” Vol. 4, August 1981) describes an experiment in which a shape factor was determined for several different nozzle designs at six levels of jet efflux velocity. Interest focused on potential differences between nozzle designs, with velocity considered as a nuisance variable. The data are shown below:

Nozzle Jet Efflux Velocity (m∕s)

Design 11.73 14.37 16.59 20.43 23.46 28.74 1 0.78 0.80 0.81 0.75 0.77 0.78 2 0.85 0.85 0.92 0.86 0.81 0.83 3 0.93 0.92 0.95 0.89 0.89 0.83 4 1.14 0.97 0.98 0.88 0.86 0.83 5 0.97 0.86 0.78 0.76 0.76 0.75

(a) Does nozzle design affect the shape factor? Compare the nozzles with a scatter plot and with an analysis of variance, using ???? = 0.05.

(b) Analyze the residuals from this experiment.

(c) Which nozzle designs are different with respect to shape factor? Draw a graph of the average shape factor for each nozzle type and compare this to a scaled t distribution.

Compare the conclusions that you draw from this plot to those from Duncan’s multiple range test.