- 13-2.13-1: 13-1. In Design and Analysis of Experiments, 5th edition (John Wile...
- 13-2.13-2: In Orthogonal Design for Process Optimization and Its Application t...
- 13-2.13-3: 13-3. The compressive strength of concrete is being studied, and fo...
- 13-2.13-4: An experiment was run to determine whether four specific firing tem...
- 13-2.13-5: 13-5. An electronics engineer is interested in the effect on tube c...
- 13-2.13-6: The response time in milliseconds was determined for three differen...
- 13-2.13-7: 13-7. An article in the ACI Materials Journal (Vol. 84, 1987, pp. 2...
- 13-2.13-8: An article in Environment International (Vol. 18, No. 4, 1992) desc...
- 13-2.13-9: 13-9. A paper in the Journal of the Association of Asphalt Paving T...
- 13-2.13-10: An article in the Materials Research Bulletin (Vol. 26, No. 11, 199...
- 13-2.13-11: Use Fishers LSD method with 0.05 to analyze the means of the five d...
- 13-2.13-12: Use Fishers LSD method with 0.05 test to analyze the means of the t...
- 13-2.13-13: Use Fishers LSD method with 0.05 to analyze the mean compressive st...
- 13-2.13-14: Use Fishers LSD method to analyze the five means for the coating ty...
- 13-2.13-15: Use Fishers LSD method to analyze the mean response times for the t...
- 13-2.13-16: Use Fishers LSD method to analyze the mean amounts of radon release...
- 13-2.13-17: Apply Fishers LSD method to the air void experiment described in Ex...
- 13-2.13-18: Apply Fishers LSD method to the superconducting material experiment...
- 13-2.13-19: 13-19. Suppose that four normal populations have common variance 2 ...
- 13-2.13-20: Suppose that five normal populations have common variance 2 100 and...
Solutions for Chapter 13-2: THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
See Arithmetic mean.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
The probability of an event given that the random experiment produces an outcome in another event.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Another name for factors that are arranged in a factorial experiment.
An expression sometimes used for nonlinear regression models or polynomial regression models.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.