- 12.1: A new medicine against hypertension was tested on 18 patients. Afte...
- 12.2: An engineering firm is involved in selecting a computer system, and...
- 12.3: The published figure for the median systolic blood pressure of midd...
- 12.4: To test the hypothesis that the median weight of 16-year-old female...
- 12.5: In 2004, the national median salary of all U.S. financial accountan...
- 12.6: An experiment was initiated to study the effect of a newly develope...
- 12.7: Determine the p-value when using the signed rank statistic in 1 and 2.
- 12.8: Twelve patients having high albumin content in their blood were tre...
- 12.9: An engineer claims that painting the exterior of a particular aircr...
- 12.10: Ten pairs of duplicate spectrochemical determinations for nickel ar...
- 12.11: Let X1, . . . , Xn be a sample from the continuous distribution F h...
- 12.12: In a study of bilingual coding, 12 bilingual (French and English) c...
- 12.13: Fifteen cities, of roughly equal size, are chosen for a traffic saf...
- 12.14: Determine the p-value in by (a) using the normal approximation; (b)...
- 12.15: The following are the weights of random samples of adult males from...
- 12.16: In a 1943 experiment (Whitlock, H. V., and Bliss, D. H., A bioassay...
- 12.17: In a 10-year study of the dispersal patterns of beavers (Sun, L. an...
- 12.18: The following data give the numbers of people who visit a local hea...
- 12.19: A production run of 50 items resulted in 11 defectives, with the de...
- 12.20: The following data represent the successive quality levels of 25 ar...
- 12.21: Can we use the runs test if we consider whether each data value is ...
- 12.22: The following table (taken from Quinn,W.H., Neal, T. V., and Antune...
Solutions for Chapter 12: Nonparametric Hypothesis Tests
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th 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
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.
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
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.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
A distribution with two modes
The joint probability distribution of two random variables.
The variance of the conditional probability distribution of a random variable.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
An expression sometimes used for nonlinear regression models or polynomial regression models.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
A matrix that provides the tests that are to be conducted in an experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Another name for a cumulative distribution function.
Error of estimation
The difference between an estimated value and the true value.
A property of a collection of events that indicates that their union equals the sample space.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
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.
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function
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