- 1.1.1: Give one possible sample of size 4 from each of the followingpopula...
- 1.1.2: For each of the following hypothetical populations, givea plausible...
- 1.1.3: Consider the population consisting of all computers of acertain bra...
- 1.1.4: a. Give three different examples of concrete populationsand three d...
- 1.1.5: Many universities and colleges have instituted supplementalinstruct...
- 1.1.6: The California State University (CSU) system consistsof 23 campuses...
- 1.1.7: A certain city divides naturally into ten district neighborhoods.Ho...
- 1.1.8: The amount of flow through a solenoid valve in an automobilespollut...
- 1.1.9: In a famous experiment carried out in 1882, Michelsonand Newcomb ob...
Solutions for Chapter 1.1: Populations, Samples, and Processes
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th 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 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.
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 equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
A chart used to organize the various potential causes of a problem. Also called a ishbone diagram.
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.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
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 .
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
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.
Another name for a probability density function
A study in which a sample from a population is used to make inference to the population. See Analytic 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.
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.