- 11.1: According to the Mendelian theory of genetics, a certain garden pea...
- 11.2: To ascertain whether a certain die was fair, 1,000 rolls of the die...
- 11.3: Determine the birth and death dates of 100 famous individuals and, ...
- 11.4: It is believed that the daily number of electrical power failures i...
- 11.5: Among 100 vacuum tubes tested, 41 had lifetimes of less than 30 hou...
- 11.6: The past output of a machine indicates that each unit it produces w...
- 11.7: The neutrino radiation from outer space was observed during several...
- 11.8: Neutrino radiation was observed over a certain period and the numbe...
- 11.9: In a certain region, insurance data indicate that 82 percent of dri...
- 11.10: A study was instigated to see if southern California earthquakes of...
- 11.11: Sometimes reported data fit a model so well that it makes one suspi...
- 11.12: Use simulation to determine the p-value and compare it with the res...
- 11.13: A sample of size 120 had a sample mean of 100 and a sample standard...
- 11.14: In 4, test the hypothesis that the daily number of failures has a P...
- 11.15: A random sample of 500 migrant families was classified by region an...
- 11.16: The following data relate the mothers age and the birthweight (in g...
- 11.17: Repeat with all of the data values doubledthat is, with these data:...
- 11.18: The number of infant mortalities as a function of the babys birthwe...
- 11.19: An experiment designed to study the relationship between hypertensi...
- 11.20: The following table shows the number of defective, acceptable, and ...
- 11.21: A sample of 300 cars having cellular phones and one of 400 cars wit...
- 11.22: To study the effect of fluoridated water supplies on tooth decay, t...
- 11.23: To determine if a malpractice lawsuit is more likely to follow cert...
- 11.24: In a famous article (S. Russell, A red sky at night. . . , Metropol...
- 11.25: Data are said to be from a lognormal distribution with parameters a...
Solutions for Chapter 11: Goodness of Fit Tests and Categorical Data Analysis
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
See Arithmetic mean.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
The mean of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
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.
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.
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Discrete random variable
A random variable with a inite (or countably ininite) range.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
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.
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.
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.