- 2.3.13: You are given n 5 measurements: 2, 1, 1,3, 5.a. Calculate the sampl...
- 2.3.14: Refer to Exercise 2.13.a. Use the data entry method in your scienti...
- 2.3.15: 2You are given n 8 measurements: 4, 1, 3, 1, 3,1, 2, 2.a. Find the ...
- 2.3.16: You are given n 8 measurements: 3, 1, 5, 6,4, 4, 3, 5.a. Calculate ...
- 2.3.17: An Archeological Find, again An article inArchaeometry involved an ...
- 2.3.18: Utility Bills in Southern CaliforniaThe monthly utility bills for a...
Solutions for Chapter 2.3: Measures of Variability
Full solutions for Introduction to Probability and Statistics 1 | 14th 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
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Coeficient of determination
See R 2 .
The mean of the conditional probability distribution of a random variable.
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 tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
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.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Defects-per-unit control chart
See U chart
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A series of tests in which changes are made to the system under study
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .