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 (blocks), with velocity considered as a nuisance variable. The data are shown below: Jet Efflux Velocity (m/s) Nozzle 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 1) Write the null hypothesis and the alternative hypothesis (for the factor). 2) Find the ANOVA table. (round to five decimal places). 3) What is your decision about the null hypothesis, consider ?.
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 (blocks), with velocity considered as a nuisance variable. The data are shown below:
| Jet Efflux Velocity (m/s) | ||||||
| Nozzle 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 |
1) Write the null hypothesis and the alternative hypothesis (for the factor).
2) Find the ANOVA table. (round to five decimal places).
3) What is your decision about the null hypothesis, consider ?.
4) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are significantly different using a familywise error rate of :
4.a) How many pairwise comparisons are possible among the treatment levels?.
4.b) Compute and .
4.c) Compute the test statistic, , for each pairwise comparison.
4.d) Write the null hypothesis and the alternative hypothesis for each pairwise comparison.
4.e) What is your decision about the null hypotheses, Explain your answers.
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