- 15.2.1: Suppose you want to use the Wilcoxon ranksum test to detect a shift...
- 15.2.2: Refer to Exercise 15.1. Suppose the alternativehypothesis is that d...
- 15.2.3: Observations from two random and independentsamples, drawn from pop...
- 15.2.4: Independent random samples of size n1 20and n2 25 are drawn from no...
- 15.2.5: Suppose you wish to detect a shift in distribution1 to the right of...
- 15.2.6: Alzheimers Disease In some tests of healthy,elderly men, a new drug...
- 15.2.7: Alzheimers, continued Refer to Exercise15.6. Suppose that two more ...
- 15.2.8: Dissolved Oxygen Content The observationsin the table are dissolved...
- 15.2.9: Eye Movement In an investigationof the visual scanning behavior of ...
- 15.2.10: Comparing NFL Quarterbacks Howdoes Aaron Rodgers, quarterback for t...
- 15.2.11: Weights of Turtles The weights ofturtles caught in two different la...
- 15.2.12: Chemotherapy Cancer treatment bymeans of chemicalschemotherapykills...
Solutions for Chapter 15.2: The Wilcoxon Rank Sum Test: Independent Random Samples
Full solutions for Introduction to Probability and Statistics 1 | 14th Edition
Solutions for Chapter 15.2: The Wilcoxon Rank Sum Test: Independent Random SamplesGet Full Solutions
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
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
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
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 variance of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
The response variable in regression or a designed experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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.
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 .
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 .