- 11.1: auto Fatalities The table below lists auto fatalities by day of the...
- 11.2: Measuring Weights When certain quantities are measured, the last di...
- 11.3: Weather-Related Deaths Listed below are the numbers of weather-rela...
- 11.4: Bicycle Helmets A study was conducted of 531 persons injured in bic...
- 11.5: Flipping and Spinning Pennies Use the data in the table below with ...
- 11.6: Home Field advantage Winning-team data were collected for teams in ...
- 11.7: Car Weight and Fuel Consumption Data Set 14 in Appendix B includes ...
- 11.8: Probability and Honesty Based on the sample described in the preced...
Solutions for Chapter 11: Chi-Square and Analysis of Variance
Full solutions for Essentials of Statistics | 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).
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
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.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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 .
Formulas used to determine the number of elements in sample spaces and events.
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.
Discrete random variable
A random variable with a inite (or countably ininite) range.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
A property of a collection of events that indicates that their union equals the sample space.
Exponential random variable
A series of tests in which changes are made to the system under study
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.
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 .