- 12.1: Lengths of Various Types of Bridges The data represent the lengths ...
- 12.2: Number of State Parks The numbers of state parks found in selected ...
- 12.3: Carbohydrates in Cereals The number of carbohydrates per serving in...
- 12.4: Grams of Fat per Serving of Pizza The number of grams of fat per se...
- 12.5: Iron Content of Foods and Drinks The iron content in three differen...
- 12.6: Temperatures in January The average January high temperatures (in d...
- 12.7: School Incidents Involving Police Calls A researcher wishes to see ...
- 12.8: Review Preparation for Statistics A statistics instructor wanted to...
- 12.9: Effects of Different Types of Diets Amedical researcher wishes to t...
- 12.10: If the null hypothesis is rejected in ANOVA, the test should be use...
- 12.11: In a two-way ANOVA, you can test main hypotheses and one interactiv...
- 12.12: Voters in Presidential Elections In a recent Presidential election,...
- 12.13: Ages of Late-Night TV Talk Show Viewers A media researcher wanted t...
- 12.14: Prices of Body Soap A consumer group desired to compare the mean pr...
- 12.15: Air Pollution A lot of different factors contribute to air pollutio...
- 12.16: Alumni Gift Solicitation Several students volunteered for an alumni...
- 12.17: Diets and Exercise Programs A researcher conducted a study of two d...
Solutions for Chapter 12: Review Execises
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th 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.
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.
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).
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.
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
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
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
The amount of variability exhibited by data
Another name for a cumulative distribution function.
A series of tests in which changes are made to the system under study
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.