- 15-3.15-20: Consider the data in Exercise 15-1 and assume that the distribution...
- 15-3.15-21: 15-21. Consider the data in Exercise 15-2. Suppose that the distrib...
- 15-3.15-22: Consider the data in Exercise 15-2. Use the largesample approximati...
- 15-3.15-23: 15-23. Consider the data in Exercise 15-3. Use the Wilcoxon signed-...
- 15-3.15-24: Consider the Rockwell hardness test data in Exercise 15-9. Assume t...
- 15-3.15-25: 15-25. Consider the paint drying time data in Exercise 15-10. Assum...
- 15-3.15-26: Apply the Wilcoxon signed-rank test to the measurement data in Exer...
- 15-3.15-27: 15-27. Apply the Wilcoxon signed-rank test to the blood cholesterol...
Solutions for Chapter 15-3: WILCOXON SIGNED-RANK TEST
Full solutions for Applied Statistics and Probability for Engineers | 3rd Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
Formulas used to determine the number of elements in sample spaces and events.
Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
Defects-per-unit control chart
See U chart
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
Exponential random variable
A series of tests in which changes are made to the system under study
A signal from a control chart when no assignable causes are present
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.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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.