- 8.6.1E: Let X1,X2, . . . ,Xn be a random sample from a normal distribution ...
- 8.6.2E: Let X1,X2, . . . ,Xn be a random sample from N(0, ?2).(a) Show that...
- 8.6.3E: Let X have an exponential distribution with a mean of ?; that is, t...
- 8.6.4E: Let X1,X2, . . . ,Xn be a random sample of Bernoulli trials b(1, p)...
- 8.6.5E: Let X1,X2, . . . ,Xn be a random sample from the normal distributio...
- 8.6.6E: Let X1,X2, . . . ,Xn be a random sample from the normal distributio...
- 8.6.7E: Let X1,X2, . . . ,X10 be a random sample of size 10 from a Poisson ...
- 188.8.131.52-1: Let X1, X2, ... , Xn be a random sample from a normal distribution ...
- 184.108.40.206-2: Let X1, X2, ... , Xn be a random sample from N(0, 2). (a) Show that...
- 220.127.116.11-3: Let X have an exponential distribution with a mean of ; that is, th...
- 18.104.22.168-4: Let X1, X2, ... , Xn be a random sample of Bernoulli trials b(1, p)...
- 22.214.171.124-5: Let X1, X2, ... , Xn be a random sample from the normal distributio...
- 126.96.36.199-6: Let X1, X2, ... , Xn be a random sample from the normal distributio...
- 188.8.131.52-7: Let X1, X2, ... , X10 be a random sample of size 10 from a Poisson ...
- 184.108.40.206-8: Consider a random sample X1, X2, ... , Xn from a distribution with ...
- 220.127.116.11-9: Let X1, X2, ... , X5 be a random sample from the Bernoulli distribu...
Solutions for Chapter 8.6: Tests of Statistical Hypotheses
Full solutions for Probability and Statistical Inference | 9th 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).
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).
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
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.
A distribution with two modes
The portion of the variability in a set of observations that is due to only random forces and which cannot be traced to speciic sources, such as operators, materials, or equipment. Also called a common cause.
Coeficient of determination
See R 2 .
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
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 dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
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 .
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.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials