- 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
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
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 tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The mean of the conditional probability distribution of a random variable.
The variance of the conditional probability distribution of a random variable.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
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 .
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
A probability distribution for a discrete random variable
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
The variance of an error term or component in a model.
Exponential random variable
A series of tests in which changes are made to the system under study
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.
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.
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 .