- 4.6.87: The accompanying normal probability plot was constructedfrom a samp...
- 4.6.88: A sample of 15 female collegiate golfers was selectedand the clubhe...
- 4.6.89: The accompanying sample consisting of n 5 20 observationson dielect...
- 4.6.90: The article A Probabilistic Model of Fracture inConcrete and Size E...
- 4.6.91: Construct a normal probability plot for the fatigue-crackpropagatio...
- 4.6.92: The article The LoadLife Relationship for M50Bearings with Silicon ...
- 4.6.93: Construct a probability plot that will allow you to assessthe plaus...
- 4.6.94: The accompanying observations are precipitation valuesduring March ...
- 4.6.95: Use a statistical software package to construct a normalprobability...
- 4.6.96: Let the ordered sample observations be denoted byy1, y2, , yn (y1 b...
- 4.6.97: The following failure time observations (1000s of hours)resulted fr...
Solutions for Chapter 4.6: Probability Plots
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
The probability of an event given that the random experiment produces an outcome in another event.
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.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
The amount of variability exhibited by data
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Fraction defective control chart
See P chart
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .