- 1.1: An election will be held next week and, by polling a sample of the ...
- 1.2: The approach used in 1(e) led to a disastrous prediction in the 193...
- 1.3: A researcher is trying to discover the average age at death for peo...
- 1.4: To determine the proportion of people in your town who are smokers,...
- 1.5: A university plans on conducting a survey of its recent graduates t...
- 1.6: An article reported that a survey of clothing worn by pedestrians k...
- 1.7: Critique Graunts method for estimating the population of London. Wh...
- 1.8: The London bills of mortality listed 12,246 deaths in 1658. Supposi...
- 1.9: Suppose you were a seller of annuities in 1662 when Graunts book wa...
- 1.10: Based on Graunts mortality table: (a) What proportion of people sur...
Solutions for Chapter 1: Introduction to Statistics
Full solutions for Introduction to Probability and Statistics for Engineers and Scientists | 5th Edition
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
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The mean of the conditional probability distribution of a random variable.
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
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
See Control chart.
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 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 .
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Defects-per-unit control chart
See U chart
The response variable in regression or a designed experiment.
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications