- 1.1: A vendor converts the weights on the packages she sends out from po...
- 1.2: Refer to Exercise 1. The vendor begins using heavier packaging, whi...
- 1.3: The specification for the pull strength of a wire that connects an ...
- 1.4: A coin is tossed twice and comes up heads both times. Someone says,...
- 1.5: The smallest number on a list is changed from 12.9 to 1.29. a. Is i...
- 1.6: There are 15 numbers on a list, and the smallest number is changed ...
- 1.7: There are 15 numbers on a list, and the mean is 25. The smallest nu...
- 1.8: The article The Selection of Yeast Strains for the Production of Pr...
- 1.9: Concerning the data represented in the following boxplot, which one...
- 1.10: True or false: In any boxplot, a. The length of the whiskers is equ...
- 1.11: For each of the following histograms, determine whether the vertica...
- 1.12: In the article Occurrence and Distribution of Ammonium in Iowa Grou...
- 1.13: The article Vehicle-Arrival Characteristics at Urban Uncontrolled I...
- 1.14: The cumulative frequency and the cumulative relative frequency for ...
- 1.15: The article Computing and Using Rural versus Urban Measures in Stat...
- 1.16: The article Hydrogeochemical Characteristics of Groundwater in a Mi...
- 1.17: Water scarcity has traditionally been a major concern in the Canary...
- 1.18: The Editors Report in the November 2003 issue of Technometrics prov...
- 1.19: The article The Ball-on-Three-Ball Test for Tensile Strength: Refin...
Solutions for Chapter 1: Sampling and Descriptive Statistics
Full solutions for Statistics for Engineers and Scientists | 4th 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.
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Bivariate normal distribution
The joint distribution of two normal random variables
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
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.
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Formulas used to determine the number of elements in sample spaces and events.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Exponential random variable
A series of tests in which changes are made to the system under study
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
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 .