- 10.2.11: An experiment to compare the spreading rates of fivedifferent brand...
- 10.2.12: In Exercise 11, suppose x3. 5 427.5. Now which trueaverage spreadin...
- 10.2.13: Repeat Exercise 12 supposing that x2. 5 502.8 in additionto x3. 5 4...
- 10.2.14: Use Tukeys procedure on the data in Example 10.3 toidentify differe...
- 10.2.15: Exercise 10.7 described an experiment in which 26 resistivityobserv...
- 10.2.16: Reconsider the axial stiffness data given in Exercise 8.ANOVA outpu...
- 10.2.17: Refer to Exercise 5. Compute a 95% t CI for u 51y2(m1 1 m2) 2 m3.
- 10.2.18: Consider the accompanying data on plant growthafter the application...
- 10.2.19: Consider a single-factor ANOVA experiment in whichI 5 3, J 5 5, x1?...
- 10.2.20: Refer to Exercise 19 and suppose x1? 5 10, x2? 5 15, andx3? 5 20. C...
- 10.2.21: The article The Effect of Enzyme Inducing Agents on theSurvival Tim...
Solutions for Chapter 10.2: Multiple Comparisons in ANOVA
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th 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 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.
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 attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
Another term for the conidence coeficient.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A probability distribution for a continuous random variable.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
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 .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
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.