- 8.1.1: Suppose that a random sample X1,...,Xn is to be taken from the unif...
- 8.1.2: . Suppose that a random sample is to be taken from the normal distr...
- 8.1.3: . Suppose that a random sample is to be taken from the normal distr...
- 8.1.4: For the conditions of Exercise 2, how large a random sample must be...
- 8.1.5: Suppose that a random sample is to be taken from the Bernoulli dist...
- 8.1.6: For the conditions of Exercise 5, use the central limit theorem in ...
- 8.1.7: For the conditions of Exercise 5, how large a random sample must be...
- 8.1.8: For the conditions of Exercise 5, how large a random sample must be...
- 8.1.9: Let X1,...,Xn be a random sample from the exponential distribution ...
Solutions for Chapter 8.1: Sampling Distributions of Estimators
Full solutions for Probability and Statistics | 4th Edition
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).
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
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).
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.
The mean of the conditional probability distribution of a random variable.
The variance of the conditional probability distribution of a random variable.
A probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
A subset of effects in a fractional factorial design that deine the aliases in the design.
A probability distribution for a discrete random variable
The amount of variability exhibited by data
Another name for a cumulative distribution function.
Error of estimation
The difference between an estimated value and the true value.
Estimate (or point estimate)
The numerical value of a point estimator.
Exponential random variable
A series of tests in which changes are made to the system under study
A signal from a control chart when no assignable causes are present
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.